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0 TD [(ed,)-13000(but)-12000(it)-12000(will)-13000(b)-1000(e)-12000(assumed)-12000(that)-12000(the)-12000(sp)-1000(eci\014cation)]TJ -210 46 TD [(of)-19000(the)-19000(probabilit)]TJ 282 0 TD [(y)-22000(space)-20000(completely)-21000(describ)-1000(es)-20000(the)-19000(p)-1000(ossible)]TJ -282 45 TD [(tra)-2000(jectories)-14000(of)]TJ /T10 1 Tf 246 0 TD (X)Tj /T11 1 Tf 47 0 TD [(in)-14000(adv)]TJ 103 0 TD [(ance,)-14000(as)-13000(w)]TJ 173 0 TD [(ell)-14000(as)-13000(their)-14000(distribution.)]TJ -569 83 TD (Eac)Tj 61 0 TD [(h)-13000(parameter)-12000(v)]TJ 234 0 TD (alue)Tj /T10 1 Tf 81 0 TD (\022)Tj /T9 1 Tf 29 0 TD (2)Tj /T11 1 Tf 37 0 TD [(\002)-11000(induces)-14000(a)-12000(corresp)-1000(onding)-15000(proba-)]TJ -442 46 TD (bilit)Tj 65 0 TD [(y)-11000(measure)]TJ /T10 1 Tf 177 0 TD (P)Tj /T8 1 Tf 25 4 TD (\022)Tj /T11 1 Tf 26 -4 TD [(on)-10000(the)-9000(underlying)-13000(measurable)-11000(space)-9000(\(\012)]TJ /T10 1 Tf 638 0 TD (;)Tj /T9 1 Tf 17 0 TD (F)Tj /T11 1 Tf 32 0 TD (\).)Tj -979.999 46 TD [(Supp)-1000(ose)-20000(that)-18000(the)-18000(measures)]TJ /T9 1 Tf 485 0 TD (f)Tj /T10 1 Tf 19 0 TD 1 Tc [(P;)-5000(P)]TJ /T8 1 Tf 68 4 TD (\022)Tj /T11 1 Tf 36 -4 TD (:)Tj /T10 1 Tf 29 0 TD (\022)Tj /T9 1 Tf 38 0 TD (2)Tj /T11 1 Tf 45 0 TD (\002)Tj /T9 1 Tf 30 0 TD (g)Tj /T11 1 Tf 37 0 TD 0 Tc [(are)-18000(m)]TJ 100 0 TD (utually)Tj -887 45 TD [(absolutely)-15000(con)]TJ 238 0 TD (tin)Tj 45 0 TD [(uous;)-14000(then)-12000(the)-13000(lik)]TJ 292 0 TD [(eliho)-1000(o)-1000(d)]TJ /T10 1 Tf 135 0 TD (L)Tj /T11 1 Tf 26 0 TD (\()Tj /T10 1 Tf 15 0 TD (\022)Tj /T11 1 Tf 19 0 TD [(\))-11000(o)0(f)-12000(the)-12000(obser-)]TJ -769.999 46 TD (v)Tj 18 0 TD (ations)Tj /T9 1 Tf 117 0 TD (O)Tj /T11 1 Tf 48 0 TD [(under)-17000(eac)]TJ 164 0 TD [(h)-17000(measure)]TJ /T10 1 Tf 191 0 TD (P)Tj /T8 1 Tf 25 4 TD (\022)Tj /T11 1 Tf 33 -4 TD (relativ)Tj 105 0 TD [(e)-19000(t)0(o)-16000(the)-17000(reference)]TJ 364 -2598 TD (measure)Tj /T10 1 Tf 150 0 TD (P)Tj /T11 1 Tf 42 0 TD [(is)-14000(w)]TJ 66 0 TD [(ell-de\014ned,)-15000(and)-13000(giv)]TJ 316 0 TD [(en)-15000(b)]TJ 73 0 TD (y)Tj /T10 1 Tf -327 100 TD (L)Tj /T11 1 Tf 26 0 TD (\()Tj /T10 1 Tf 15 0 TD (\022)Tj /T11 1 Tf 19 0 TD 11 Tc (\)=)Tj /T10 1 Tf 67 0 TD (E)Tj /T5 1 Tf 36 -45 TD (n)Tj /T10 1 Tf 38 21 TD 0 Tc (dP)Tj /T8 1 Tf 45 4 TD (\022)Tj ET 438.24 681.11 14.88 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 439.68 672.47 Tm (dP)Tj /T5 1 Tf 61 -72 TD (\014)Tj 0 25 TD (\014)Tj T* (\014)Tj /T9 1 Tf 20 -3 TD (O)Tj /T5 1 Tf 31 -45 TD (o)Tj /T10 1 Tf 35 45 TD (:)Tj /T11 1 Tf -674 97 TD [(Adopting)-17000(a)-16000(maxim)]TJ 319 0 TD (um-lik)Tj 105 0 TD [(eli)-1000(ho)-1000(o)-2000(d)-18000(approac)]TJ 269 0 TD [(h,)-17000(w)]TJ 76 0 TD [(e)-15000(wish)-17000(to)-15000(\014nd)]TJ -768.999 46 TD [(an)-13000(optim)]TJ 149 0 TD [(um)-15000(v)]TJ 86 0 TD (alue)Tj /T10 1 Tf 81 0 TD (\022)Tj /T8 1 Tf 19 -16 TD (?)Tj /T9 1 Tf 29 16 TD (2)Tj /T11 1 Tf 36 0 TD [(\002)-13000(maximizing)]TJ /T10 1 Tf 249 0 TD (L)Tj /T11 1 Tf 26 0 TD (\()Tj /T10 1 Tf 15 0 TD (\022)Tj /T11 1 Tf 19 0 TD [(\).)-17000(In)-13000(general,)-14000(this)]TJ -709 45 TD [(is)-12000(a)-12000(di\016cult)-14000(problem,)-13000(and)-13000(it)-12000(ma)]TJ 527.999 0 TD [(y)-12000(not)-12000(b)-1000(e)-12000(p)-1000(ossible)-15000(to)-11000(obtain)-14000(a)]TJ -527.999 46 TD [(closed-form)-11000(expression)-11000(for)]TJ /T10 1 Tf 438 0 TD (\022)Tj /T8 1 Tf 19 -16 TD (?)Tj /T11 1 Tf 18 16 TD [(.)-16000(The)]TJ /T3 1 Tf 102 0 TD [(EM)-11000(algorithm)]TJ /T11 1 Tf 239 0 TD [([6])-9000(pro)]TJ 104 0 TD (vides)Tj -920 46 TD [(an)-9000(alternativ)]TJ 209 0 TD [(e)-11000(approac)]TJ 158 0 TD [(h,)-11000(whereb)]TJ 161 0 TD [(y)-10000(a)-9000(sequence)-10000(of)-8000(estimates)]TJ 421 -10 TD (^)Tj /T10 1 Tf -4 10 TD (\022)Tj /T11 1 Tf 30 0 TD (=)Tj /T9 1 Tf -975 45 TD (f)Tj /T11 1 Tf 22 -10 TD (^)Tj /T10 1 Tf -3 10 TD (\022)Tj /T8 1 Tf 18 4 TD (m)Tj /T11 1 Tf 44 -4 TD (:)Tj /T10 1 Tf 26 0 TD (m)Tj /T11 1 Tf 49 0 TD 15 Tc (=1)Tj /T10 1 Tf 64 0 TD (;)Tj /T11 1 Tf 17 0 TD (2)Tj /T10 1 Tf 19 0 TD 6 Tc [(;::)-1000(:)]TJ /T9 1 Tf 62 0 TD (g)Tj /T11 1 Tf 35 0 TD 0 Tc [(is)-16000(constructed)-17000(recursiv)]TJ 380 0 TD (ely)Tj 44 0 TD 18 Tc (,b)Tj 49 0 TD 16 Tc (yc)Tj 52 0 TD 0 Tc [(ho)-1000(osing)]TJ -874.999 36 TD (^)Tj /T10 1 Tf -3 10 TD (\022)Tj /T8 1 Tf 18 4 TD (m)Tj /T7 1 Tf 27 0 TD (+1)Tj /T11 1 Tf 54 -4 TD [(to)-13000(maximize)-14000(an)-14000(auxiliary)-16000(Q-function)]TJ /T10 1 Tf 624.999 0 TD (Q)Tj /T11 1 Tf 30 0 TD (\()Tj /T10 1 Tf 15 0 TD 1 Tc (\022;)Tj /T11 1 Tf 39.001 -10 TD (^)Tj /T10 1 Tf -3 10 TD (\022)Tj /T8 1 Tf 18 4 TD (m)Tj /T11 1 Tf 29 -4 TD 0 Tc [(\))-13000([7])-12000([8];)]TJ /T10 1 Tf -648 111 TD (Q)Tj /T11 1 Tf 30 0 TD (\()Tj /T10 1 Tf 15 0 TD (\022)Tj /T7 1 Tf 18 4 TD (1)Tj /T10 1 Tf 18 -4 TD 6 Tc (;\022)Tj /T7 1 Tf 35 4 TD (2)Tj /T11 1 Tf 17 -4 TD (\))Tj /T6 1 Tf 58 -23 TD (4)Tj /T11 1 Tf -2 23 TD (=)Tj /T10 1 Tf 72 0 TD (E)Tj /T8 1 Tf 28 4 TD (\022)Tj /T2 1 Tf 15 5 TD (2)Tj /T5 1 Tf 25 -66 TD (\032)Tj /T11 1 Tf 31 57 TD 0 Tc (ln)Tj /T10 1 Tf 48 -24 TD (dP)Tj /T8 1 Tf 45 4 TD (\022)Tj /T2 1 Tf 15 5 TD (1)Tj ET 460.08 565.19 18.72 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 460.08 556.55 Tm (dP)Tj /T8 1 Tf 45 4 TD (\022)Tj /T2 1 Tf 15 5 TD (2)Tj /T5 1 Tf 22 -94 TD (\014)Tj 0 25 TD (\014)Tj T* (\014)Tj T* (\014)Tj /T9 1 Tf 21 -16 TD (O)Tj /T5 1 Tf 31 -57 TD (\033)Tj /T10 1 Tf 38 57 TD (;)Tj /T11 1 Tf -515 84 TD (^)Tj /T10 1 Tf -3 9 TD (\022)Tj /T8 1 Tf 18 4 TD (m)Tj /T7 1 Tf 27 0 TD (+1)Tj /T11 1 Tf 82 -4 TD (=)Tj 72 0 TD [(arg)-7000(max)]TJ /T8 1 Tf 66 25 TD (\022)Tj /T6 1 Tf 16 0 TD (2)Tj /T7 1 Tf 21 0 TD (\002)Tj /T10 1 Tf 35 -25 TD (Q)Tj /T11 1 Tf 30 0 TD (\()Tj /T10 1 Tf 15 0 TD 1 Tc (\022;)Tj /T11 1 Tf 40 -9 TD (^)Tj /T10 1 Tf -4 9 TD (\022)Tj /T8 1 Tf 18 4 TD (m)Tj /T11 1 Tf 30 -4 TD (\))Tj /T10 1 Tf 15 0 TD (:)Tj /T11 1 Tf -747 110 TD 0 Tc [(Under)-9000(suitable)-11000(regularit)]TJ 391 0 TD [(y)-11000(conditions)-11000(on)]TJ /T10 1 Tf 259 0 TD (Q)Tj /T11 1 Tf 30 0 TD (\()Tj /T9 1 Tf 15 0 TD (\001)Tj /T10 1 Tf 11 0 TD (;)Tj /T9 1 Tf 17 0 TD (\001)Tj /T11 1 Tf 11 0 TD [(\),)-9000(the)-9000(sequence)]TJ 255.001 -9 TD (^)Tj /T10 1 Tf -3 9 TD (\022)Tj /T11 1 Tf -986 46 TD [(can)-10000(b)-1000(e)-10000(sho)]TJ 170 0 TD [(wn)-10000(to)-10000(con)]TJ 159 0 TD (v)Tj 19 0 TD [(erge)-11000(to)-9000(a)-10000(stationary)-12000(p)-1000(oin)]TJ 402 0 TD [(t)-11000(o)0(f)-9000(the)-10000(original)]TJ -749.999 46 TD (lik)Tj 39 0 TD [(eliho)-2000(o)-1000(d)-18000(function,)-17000(and)-16000(maximization)-19000(of)-15000(the)-15000(Q-function)-17000(at)]TJ -39 45 TD (eac)Tj 52 0 TD [(h)-15000(iteration)-17000(is)-16000(usually)-17000(easier)-16000(than)-16000(direct)-16000(maximization)-18000(of)]TJ /T10 1 Tf -52 46 TD (L)Tj /T11 1 Tf 26 0 TD (\()Tj /T9 1 Tf 15 0 TD (\001)Tj /T11 1 Tf 11 0 TD [(\).)-30000(Applying)-20000(the)-17000(EM)-18000(algorithm)-19000(to)-18000(the)-17000(mo)-1000(del)-19000(describ)-1000(ed)]TJ -52 46 TD [(ab)-1000(o)]TJ 59 0 TD (v)Tj 19 0 TD [(e,)-13000(and)-14000(ignoring)-16000(constan)]TJ 392 0 TD [(ts,)-13000(the)-13000(Q-function)-14000(is)-14000(giv)]TJ 400 0 TD [(en)-14000(b)]TJ 72 0 TD (y)Tj /T10 1 Tf -941.999 126 TD (Q)Tj /T11 1 Tf 30 0 TD (\()Tj /T10 1 Tf 15 0 TD (\022)Tj /T7 1 Tf 18 4 TD (1)Tj /T10 1 Tf 17 -4 TD 7 Tc (;\022)Tj /T7 1 Tf 36 4 TD (2)Tj /T11 1 Tf 17 -4 TD 10 Tc (\)=)Tj /T10 1 Tf 66 0 TD (E)Tj /T8 1 Tf 28 4 TD (\022)Tj /T2 1 Tf 15 5 TD (2)Tj /T9 1 Tf 18 -9 TD (f)Tj /T8 1 Tf 29 -51 TD (N)Tj /T4 1 Tf 24 4 TD (o)Tj /T5 1 Tf -34 9 TD (X)Tj /T8 1 Tf 1 87 TD (n)Tj /T7 1 Tf 19 0 TD 0 Tc (=1)Tj /T8 1 Tf 47 -102 TD (N)Tj /T7 1 Tf 27 0 TD (\()Tj /T8 1 Tf 12 0 TD (n)Tj /T7 1 Tf 19 0 TD (\))Tj /T5 1 Tf -53 15 TD (X)Tj /T8 1 Tf 2 87 TD (k)Tj /T7 1 Tf 17 0 TD (=1)Tj /T11 1 Tf 46 -49 TD (\([)Tj /T10 1 Tf 26 0 TD (y)Tj /T8 1 Tf 20 -18 TD (n)Tj -1 25 TD (k)Tj /T9 1 Tf 30 -7 TD (\000)Tj ET 440.4 436.55 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 440.4 428.87 Tm (H)Tj /T8 1 Tf 34 4 TD (\022)Tj /T2 1 Tf 15 5 TD (2)Tj ET 456.48 436.55 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 456.48 428.87 Tm (X)Tj /T8 1 Tf 35 -23 TD (n)Tj 0 30 TD (k)Tj /T11 1 Tf 21 -7 TD (])Tj /T8 1 Tf 11 -18 TD (T)Tj /T11 1 Tf 24 18 TD (\006)Tj /T6 1 Tf 28 -18 TD (\000)Tj /T7 1 Tf 24 0 TD (1)Tj /T8 1 Tf -24 25 TD (w)Tj /T11 1 Tf 41 -7 TD ([)Tj /T10 1 Tf 11 0 TD (y)Tj /T8 1 Tf 20 -18 TD (n)Tj -1 25 TD (k)Tj /T9 1 Tf 31 -7 TD (\000)Tj ET 518.64 436.55 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 518.64 428.87 Tm (H)Tj /T8 1 Tf 35 4 TD (\022)Tj /T2 1 Tf 15 5 TD (2)Tj ET 534.96 436.55 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 534.96 428.87 Tm (X)Tj /T8 1 Tf 35 -23 TD (n)Tj 0 30 TD (k)Tj /T11 1 Tf 21 -7 TD (])Tj /T9 1 Tf -666 105 TD (\000)Tj /T11 1 Tf 30 0 TD ([)Tj /T10 1 Tf 11 0 TD (y)Tj /T8 1 Tf 20 -18 TD (n)Tj -1 24 TD (k)Tj /T9 1 Tf 30 -6 TD (\000)Tj ET 419.52 411.59 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 419.52 403.67 Tm (H)Tj /T8 1 Tf 34 4 TD (\022)Tj /T2 1 Tf 15 5 TD (1)Tj ET 435.6 411.59 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 435.6 403.67 Tm (X)Tj /T8 1 Tf 35 -24 TD (n)Tj 0 30 TD (k)Tj /T11 1 Tf 21 -6 TD (])Tj /T8 1 Tf 11 -18 TD (T)Tj /T11 1 Tf 24 18 TD (\006)Tj /T6 1 Tf 28 -18 TD (\000)Tj /T7 1 Tf 24 0 TD (1)Tj /T8 1 Tf -24 24 TD (w)Tj /T11 1 Tf 41 -6 TD ([)Tj /T10 1 Tf 11 0 TD (y)Tj /T8 1 Tf 20 -18 TD (n)Tj -1 24 TD (k)Tj /T9 1 Tf 31 -6 TD (\000)Tj ET 497.76 411.59 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 497.76 403.67 Tm (H)Tj /T8 1 Tf 35 4 TD (\022)Tj /T2 1 Tf 15 5 TD (1)Tj ET 514.08 411.59 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 514.08 403.67 Tm (X)Tj /T8 1 Tf 35 -24 TD (n)Tj 0 30 TD (k)Tj /T11 1 Tf 21 -6 TD (]\))Tj /T9 1 Tf 26 0 TD [(jO)-1000(g)]TJ /T10 1 Tf 61 0 TD (:)Tj /T11 1 Tf -980 84 TD [(Neglecting)-15000(terms)-13000(not)-13000(in)]TJ 394 0 TD (v)Tj 19 0 TD (olving)Tj /T10 1 Tf 115 0 TD (\022)Tj /T7 1 Tf 18 4 TD (1)Tj /T11 1 Tf 18 -4 TD [(,)-12000(this)-14000(can)-13000(b)-1000(e)-14000(re-written)-13000(as)]TJ /T10 1 Tf -564 91 TD (Q)Tj /T11 1 Tf 30 0 TD (\()Tj /T10 1 Tf 15 0 TD (\022)Tj /T7 1 Tf 18 4 TD (1)Tj /T10 1 Tf 17 -4 TD 7 Tc (;\022)Tj /T7 1 Tf 36 4 TD (2)Tj /T11 1 Tf 17 -4 TD 0 Tc [(\))-10000(=)-11000(tr)-9000(\006)]TJ /T6 1 Tf 133 -18 TD (\000)Tj /T7 1 Tf 24 0 TD (1)Tj /T8 1 Tf -24 25 TD (w)Tj /T11 1 Tf 41 -7 TD (\()Tj ET 390.48 369.35 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 390.48 361.67 Tm (H)Tj /T8 1 Tf 34 4 TD (\022)Tj /T2 1 Tf 15 5 TD (1)Tj /T9 1 Tf 18 -9 TD (Z)Tj /T8 1 Tf 31 -18 TD (b)Tj -3 25 TD (\022)Tj /T2 1 Tf 15 5 TD (2)Tj /T8 1 Tf 18 -30 TD (T)Tj /T11 1 Tf 24 18 TD (+)Tj /T9 1 Tf 30 0 TD (Z)Tj /T8 1 Tf 31 -18 TD (b)Tj -3 25 TD (\022)Tj /T2 1 Tf 15 5 TD (2)Tj ET 448.8 369.35 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 448.8 361.67 Tm (H)Tj /T8 1 Tf 35 -23 TD (T)Tj 0 30 TD (\022)Tj /T2 1 Tf 15 5 TD (1)Tj /T9 1 Tf 18 -12 TD (\000)Tj ET 472.32 369.35 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 472.32 361.67 Tm (H)Tj /T8 1 Tf 35 4 TD (\022)Tj /T2 1 Tf 15 5 TD (1)Tj /T9 1 Tf 18 -9 TD (Z)Tj /T8 1 Tf 31 -18 TD (a)Tj -3 25 TD (\022)Tj /T2 1 Tf 15 5 TD (2)Tj ET 503.28 369.35 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 503.28 361.67 Tm (H)Tj /T8 1 Tf 34 -23 TD (T)Tj 0 30 TD (\022)Tj /T2 1 Tf 15 5 TD (1)Tj /T11 1 Tf 18 -12 TD (\)+)Tj /T10 1 Tf 45 0 TD (K)Tj /T11 1 Tf 36 0 TD (\()Tj /T10 1 Tf 15 0 TD (\022)Tj /T7 1 Tf 18 4 TD (2)Tj /T11 1 Tf 17 -4 TD (\))Tj -990 85 TD (where)Tj /T10 1 Tf 111 0 TD (K)Tj /T11 1 Tf 36 0 TD (\()Tj /T10 1 Tf 15 0 TD (\022)Tj /T7 1 Tf 18 4 TD (2)Tj /T11 1 Tf 16 -4 TD [(\))-13000(i)0(s)-14000(a)-13000(function)-14000(of)]TJ /T10 1 Tf 293 0 TD (\022)Tj /T7 1 Tf 18 4 TD (2)Tj /T11 1 Tf 30 -4 TD [(alone,)-14000(and)-14000(w)]TJ 213 0 TD [(e)-12000(de\014ne)]TJ /T9 1 Tf -550 129 TD (Z)Tj /T8 1 Tf 31 -18 TD (a)Tj -3 24 TD (\022)Tj /T6 1 Tf 64 -30 TD (4)Tj /T11 1 Tf -1 24 TD (=)Tj /T8 1 Tf 81 -52 TD (N)Tj /T4 1 Tf 24 4 TD (o)Tj /T5 1 Tf -34 9 TD (X)Tj /T8 1 Tf 2 87 TD (n)Tj /T7 1 Tf 19 0 TD (=1)Tj /T8 1 Tf 46 -102 TD (N)Tj /T7 1 Tf 27 0 TD (\()Tj /T8 1 Tf 12 0 TD (n)Tj /T7 1 Tf 19 0 TD (\))Tj /T5 1 Tf -53 15 TD (X)Tj /T8 1 Tf 2 87 TD (k)Tj /T7 1 Tf 17 0 TD (=1)Tj /T10 1 Tf 52 -48 TD (E)Tj /T8 1 Tf 28 4 TD (\022)Tj /T9 1 Tf 18 -4 TD (f)Tj ET 450 318.23 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 450 310.31 Tm (X)Tj /T8 1 Tf 35 -24 TD (n)Tj 0 30 TD (k)Tj ET 463.44 318.23 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 463.44 310.31 Tm (X)Tj /T8 1 Tf 35 -24 TD (n)Tj 0 30 TD (k)Tj 21 -24 TD (T)Tj /T9 1 Tf 24 18 TD (jO)Tj /T8 1 Tf 41 4 TD (n)Tj /T9 1 Tf 22 -4 TD (g)Tj /T10 1 Tf 19 0 TD (;)Tj /T9 1 Tf -585 145 TD (Z)Tj /T8 1 Tf 31 -18 TD (b)Tj -3 25 TD (\022)Tj /T6 1 Tf 61 -30 TD (4)Tj /T11 1 Tf -1 23 TD (=)Tj /T8 1 Tf 81 -51 TD (N)Tj /T4 1 Tf 24 4 TD (o)Tj /T5 1 Tf -34 9 TD (X)Tj /T8 1 Tf 2 87 TD (n)Tj /T7 1 Tf 19 0 TD (=1)Tj /T8 1 Tf 46 -102 TD (N)Tj /T7 1 Tf 27 0 TD (\()Tj /T8 1 Tf 12 0 TD (n)Tj /T7 1 Tf 19 0 TD (\))Tj /T5 1 Tf -53 15 TD (X)Tj /T8 1 Tf 2 87 TD (k)Tj /T7 1 Tf 17 0 TD (=1)Tj /T10 1 Tf 52 -49 TD (y)Tj /T8 1 Tf 20 -18 TD (n)Tj -1 25 TD (k)Tj /T10 1 Tf 23 -7 TD (E)Tj /T8 1 Tf 28 4 TD (\022)Tj /T9 1 Tf 18 -4 TD (f)Tj ET 460.08 283.19 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 460.08 275.51 Tm (X)Tj /T8 1 Tf 34 -23 TD (n)Tj 0 30 TD (k)Tj /T9 1 Tf 22 -7 TD (jO)Tj /T8 1 Tf 41 4 TD (n)Tj /T9 1 Tf 21 -4 TD (g)Tj /T8 1 Tf 19 -18 TD (T)Tj /T10 1 Tf 25 18 TD (:)Tj /T11 1 Tf -774 132 TD [(The)-14000(\014rst)-14000(term)-14000(in)]TJ /T10 1 Tf 299 0 TD (Q)Tj /T11 1 Tf 30 0 TD (\()Tj /T10 1 Tf 15 0 TD 1 Tc (\022;)Tj /T11 1 Tf 39 -10 TD (^)Tj /T10 1 Tf -3 10 TD (\022)Tj /T8 1 Tf 18 4 TD (m)Tj /T11 1 Tf 30 -4 TD 0 Tc [(\))-13000(con)]TJ 84 0 TD [(tains)-16000(a)-14000(negativ)]TJ 249 0 TD [(e)-16000(semi-de\014nite)]TJ -761 46 TD [(quadratic)-13000(form)-11000(in)]TJ /T10 1 Tf 303 0 TD (H)Tj /T8 1 Tf 32 4 TD (\022)Tj /T11 1 Tf 17 -4 TD [(,)-11000(and)-12000(can)-12000(b)-1000(e)-12000(maximized)-14000(using)-13000(standard)]TJ -352 45 TD [(optimization)-20000(tec)]TJ 276 0 TD [(hniques,)-19000(pro)]TJ 209 0 TD [(vided)-18000(that)]TJ /T9 1 Tf 194 0 TD (Z)Tj /T8 1 Tf 31.001 -15 TD (a)Tj -3 23 TD (\022)Tj /T11 1 Tf 38 -8 TD [(is)-17000(non-singular.)]TJ -745 46 TD [(Conditions)-16000(ensuring)-16000(that)-14000(the)-13000(problem)-15000(is)-15000(w)]TJ 716.999 0 TD [(ell-p)-1000(osed)-15000(will)-16000(not)]TJ -716.999 46 TD [(b)-1000(e)-16000(discussed)-18000(here.)-25000(Di\013eren)]TJ 461 0 TD (tiating)Tj /T10 1 Tf 128 0 TD (Q)Tj /T11 1 Tf 30 0 TD (\()Tj /T10 1 Tf 15 0 TD 1 Tc (\022;)Tj /T11 1 Tf 39 -10 TD (^)Tj /T10 1 Tf -3 10 TD (\022)Tj /T8 1 Tf 18 4 TD (m)Tj /T11 1 Tf 30 -4 TD 0 Tc [(\))-15000(w.r.t.)-24000(eac)]TJ 197 0 TD [(h)-16000(pa-)]TJ -915 45 TD [(rameter)-15000(in)]TJ ET 359.04 196.79 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 359.04 189.11 Tm (H)Tj /T8 1 Tf 35 4 TD (\022)Tj /T11 1 Tf 32 -4 TD [(and)-16000(setting)-15000(the)-15000(result)-16000(to)-15000(zero)-15000(under)-15000(this)-16000(as-)]TJ -258 46 TD [(sumption)-18000(giv)]TJ 220 0 TD [(es)-17000(the)-16000(new)-16000(estimate)]TJ ET 451.44 185.75 8.4 -0.48 re f BT /T10 1 Tf 0.24 0 0 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[(es)-20000(determining)-22000(the)-18000(general)-20000(class)-20000(of)]TJ -397 46 TD [(conditional)-17000(exp)-1000(ectations)]TJ /T10 1 Tf 421 0 TD (E)Tj /T9 1 Tf 30 0 TD (f)Tj /T10 1 Tf 19 0 TD (\036)Tj /T11 1 Tf 23 0 TD (\()Tj /T10 1 Tf 15 0 TD (X)Tj /T8 1 Tf 32 4 TD (k)Tj /T11 1 Tf 19 -4 TD (\))Tj /T9 1 Tf 15 0 TD (jF)Tj /T8 1 Tf 43 -16 TD (Y)Tj -4 22 TD (n)Tj /T9 1 Tf 30 -6 TD (g)Tj /T11 1 Tf 32 0 TD [(of)-13000(measurable)-16000(func-)]TJ -675 45 TD [(tionals)-13000(of)-11000(the)]TJ /T10 1 Tf 228 0 TD (X)Tj /T11 1 Tf 46 0 TD [(pro)-1000(cess.)-17000(The)-11000(conditional)-14000(la)]TJ 449 0 TD 12 Tc [(wo)12000(f)1000(X)12000(,)]TJ /T10 1 Tf 132 0 TD (P)Tj /T8 1 Tf 25 10 TD (X)Tj /T4 1 Tf 25 6 TD (k)Tj /T6 1 Tf 18 -6 TD 0 Tc (jF)Tj /T4 1 Tf 34 -8 TD (Y)Tj -3 15 TD (n)Tj /T11 1 Tf 40 -17 TD (:)Tj /T9 1 Tf -994 46 TD (B)Tj /T11 1 Tf 26 0 TD (\(I)Tj 23 0 TD (R)Tj /T8 1 Tf 28 -16 TD (p)Tj /T11 1 Tf 18 16 TD (\))Tj /T9 1 Tf 26 0 TD (!)Tj /T11 1 Tf 49 0 TD ([0)Tj /T10 1 Tf 30 0 TD (;)Tj /T11 1 Tf 17 0 TD [(1],)-12000(is)-14000(obtained)-14000(as)-14000(a)-13000(s)0(p)-1000(ecial)-15000(case)-13000(b)]TJ 555 0 TD [(y)-13000(noting)-15000(that)]TJ /T10 1 Tf -727 78 TD (P)Tj /T8 1 Tf 25 10 TD (X)Tj /T4 1 Tf 25 6 TD (k)Tj /T6 1 Tf 18 -6 TD (jF)Tj /T4 1 Tf 34 -8 TD (Y)Tj -3 15 TD (n)Tj /T11 1 Tf 30 -17 TD (\()Tj /T10 1 Tf 15 0 TD (A)Tj /T11 1 Tf 29 0 TD (\))Tj 56 0 TD (=)Tj /T10 1 Tf 71 0 TD (E)Tj /T9 1 Tf 30 0 TD (f)Tj /T10 1 Tf 19 0 TD (I)Tj /T11 1 Tf 20 0 TD (\()Tj /T10 1 Tf 15 0 TD (X)Tj /T8 1 Tf 32 4 TD (k)Tj /T9 1 Tf 30 -4 TD (2)Tj /T10 1 Tf 36 0 TD (A)Tj /T11 1 Tf 29 0 TD (\))Tj /T9 1 Tf 15 0 TD (jF)Tj /T8 1 Tf 43 -18 TD (Y)Tj -4 25 TD (n)Tj /T9 1 Tf 30 -7 TD (g)Tj /T11 1 Tf 55 0 TD (:)Tj /T9 1 Tf 47 0 TD (8)Tj /T10 1 Tf 21 0 TD (A)Tj /T9 1 Tf 40 0 TD 10 Tc (2B)Tj /T11 1 Tf 62 0 TD 0 Tc (\(I)Tj 23 0 TD (R)Tj /T8 1 Tf 28 -18 TD (p)Tj /T11 1 Tf 18 18 TD (\))Tj /T10 1 Tf 15 0 TD (;)Tj /T11 1 Tf -949 79 TD [(and)-10000(con)]TJ 127 0 TD [(tains)-12000(all)-11000(information)-12000(ab)-1000(out)-11000(the)]TJ /T10 1 Tf 516 0 TD (X)Tj /T11 1 Tf 45 0 TD [(pro)-1000(cess)-10000(that)-10000(can)-11000(b)-1000(e)]TJ -687.999 45 TD [(extracted)-15000(from)-13000(measuremen)]TJ 466.999 0 TD 15 Tc [(to)15000(f)]TJ /T10 1 Tf 75 0 TD (Y)Tj /T7 1 Tf 22 4 TD (1)Tj /T10 1 Tf 24 -4 TD 6 Tc (:::Y)Tj /T8 1 Tf 73 4 TD (n)Tj /T11 1 Tf 22 -4 TD 0 Tc [(.)-20000(I)0(t)-13000(i)0(s)-15000(o)0(f)-14000(particular)]TJ -683 46 TD (in)Tj 30 0 TD [(terest)-19000(to)-18000(consider)-20000(cases)-19000(where)-18000(this)-19000(measure)-19000(\(or)-18000(the)-18000(cor-)]TJ -30 46 TD [(resp)-1000(onding)-17000(densit)]TJ 295 0 TD [(y)-16000(function,)-15000(if)-15000(it)-15000(exists\))-15000(can)-15000(b)-1000(e)-14000(propagated)]TJ -295 45 TD (recursiv)Tj 129 0 TD [(ely)-15000(from)-11000(the)-13000(measuremen)]TJ 422 0 TD [(ts.)-18000(T)]TJ 84 0 TD [(emp)-1000(oral)-13000(correlation)-14000(in)]TJ -634.999 46 TD (the)Tj /T10 1 Tf 67 0 TD (X)Tj /T11 1 Tf 48 0 TD (and)Tj /T10 1 Tf 75 0 TD (Y)Tj /T11 1 Tf 45 0 TD [(pro)-1000(cesses)-14000(mak)]TJ 236 0 TD [(es)-15000(it)-14000(di\016cult)-15000(to)-14000(accomplish)-16000(this)]TJ -471 46 TD [(directly;)-21000(b)]TJ 177 0 TD 17 Tc [(yi)17000(n)]TJ 67 0 TD 0 Tc [(tro)-1000(ducing)-20000(a)-18000(new)-17000(probabilit)]TJ 459 0 TD [(y)-20000(measure,)-19000(under)]TJ -702.999 45 TD (whic)Tj 75 0 TD (h)Tj /T10 1 Tf 36 0 TD (Y)Tj /T11 1 Tf 44 0 TD [(is)-15000(an)-14000(i.i.d.)-21000(pro)-1000(cess)-15000(indep)-1000(enden)]TJ 511 0 TD 16 Tc [(to)16000(f)]TJ /T10 1 Tf 76 0 TD (X)Tj /T11 1 Tf 35 0 TD 0 Tc [(,)-13000(the)-14000(problem)]TJ -777 46 TD [(can)-11000(b)-1000(e)-12000(circum)]TJ 230 0 TD (v)Tj 19 0 TD (en)Tj 37 0 TD [(ted.)-18000(This)-11000(idea)-12000(is)-12000(originally)-14000(due)-12000(to)-11000(Br)]TJ 606.999 0 TD (\023)Tj 1 0 TD (emaud)Tj 171.001 -2598 TD [(and)-13000(v)]TJ 92 0 TD [(an)-14000(Sc)]TJ 91 0 TD (h)Tj 20 0 TD [(upp)-1000(en)-14000([10],)-12000(and)-14000(w)]TJ 301 0 TD [(as)-12000(later)-14000(dev)]TJ 193 0 TD [(elop)-1000(ed)-15000(in)-13000([11])-13000([12].)]TJ -696.999 45 TD [(Here)-12000(w)]TJ 117 0 TD [(e)-11000(duplicate)-14000(the)-12000(approac)]TJ 388 0 TD [(h)-13000(used)-13000(b)]TJ 141 0 TD [(y)-12000(Elliott)-14000([12],)-11000(to)-12000(yield)]TJ -645.999 46 TD (recursiv)Tj 129 0 TD [(e)-13000(smo)-1000(othing)-14000(form)]TJ 293 0 TD [(ulae)-13000(for)-12000(our)-13000(mo)-1000(del.)-17000(First)-13000(construct)]TJ -422 45 TD [(pro)-1000(cesses)]TJ /T10 1 Tf 166 0 TD (\025)Tj /T11 1 Tf 33 0 TD (=)Tj /T9 1 Tf 41 0 TD (f)Tj /T10 1 Tf 19 0 TD (\025)Tj /T8 1 Tf 22 4 TD (n)Tj /T11 1 Tf 32 -4 TD (:)Tj /T10 1 Tf 22 0 TD (n)Tj /T9 1 Tf 33 0 TD (2)Tj /T11 1 Tf 37 0 TD (I)Tj 7 0 TD (N)Tj /T9 1 Tf 29 0 TD (g)Tj /T11 1 Tf 19 0 TD 13 Tc [(,\003)3000(=)]TJ /T9 1 Tf 101 0 TD (f)Tj /T11 1 Tf 19 0 TD (\003)Tj /T8 1 Tf 27 4 TD (n)Tj /T11 1 Tf 32 -4 TD (:)Tj /T10 1 Tf 21 0 TD (n)Tj /T9 1 Tf 34 0 TD (2)Tj /T11 1 Tf 37 0 TD (I)Tj 7 0 TD (N)Tj /T9 1 Tf 29 0 TD (g)Tj /T11 1 Tf 19 0 TD 0 Tc [(,)-12000(where)]TJ /T10 1 Tf -723 89 TD (\025)Tj /T8 1 Tf 22 4 TD (n)Tj /T6 1 Tf 64 -27 TD (4)Tj /T11 1 Tf -1 23 TD (=)Tj 72 0 TD (exp\()Tj 78 -24 TD (1)Tj ET 384.72 651.11 4.8 -0.48 re f BT /T11 1 Tf 0.24 0 0 -0.24 384.72 642.47 Tm (2)Tj /T10 1 Tf 24 -25 TD (h)Tj /T11 1 Tf 22 0 TD (\()Tj /T10 1 Tf 15 0 TD (X)Tj /T8 1 Tf 32 4 TD (n)Tj /T11 1 Tf 21 -4 TD (\))Tj /T8 1 Tf 15 -18 TD (T)Tj /T11 1 Tf 25 18 TD (\006)Tj /T6 1 Tf 28 -18 TD (\000)Tj /T7 1 Tf 24 0 TD (1)Tj /T8 1 Tf -24 25 TD (w)Tj /T10 1 Tf 41 -7 TD (h)Tj /T11 1 Tf 22 0 TD (\()Tj /T10 1 Tf 15 0 TD (X)Tj /T8 1 Tf 32 4 TD (n)Tj /T11 1 Tf 21 -4 TD (\))Tj /T9 1 Tf 23 0 TD (\000)Tj /T10 1 Tf 38 0 TD (h)Tj /T11 1 Tf 22 0 TD (\()Tj /T10 1 Tf 15 0 TD (X)Tj /T8 1 Tf 32 4 TD (n)Tj /T11 1 Tf 21 -4 TD (\))Tj /T8 1 Tf 15 -18 TD (T)Tj /T11 1 Tf 25 18 TD (\006)Tj /T6 1 Tf 28 -18 TD (\000)Tj /T7 1 Tf 24 0 TD (1)Tj /T8 1 Tf -24 25 TD (w)Tj /T10 1 Tf 41 -7 TD (Y)Tj /T8 1 Tf 22 4 TD (n)Tj /T11 1 Tf 21 -4 TD (\))Tj /T10 1 Tf 15 0 TD (;)Tj /T11 1 Tf -870 87 TD (\003)Tj /T8 1 Tf 27 4 TD (n)Tj /T6 1 Tf 63 -28 TD (4)Tj /T11 1 Tf -1 24 TD (=)Tj 72 0 TD (\005)Tj /T8 1 Tf 29 5 TD (k)Tj /T6 1 Tf 17 0 TD (\024)Tj /T8 1 Tf 24 0 TD (n)Tj /T10 1 Tf 21 -5 TD (\025)Tj /T8 1 Tf 22 4 TD (k)Tj /T10 1 Tf 19 -4 TD (:)Tj /T11 1 Tf -352 72 TD [(Under)-9000(the)-9000(original)-12000(measure)]TJ /T10 1 Tf 453.999 0 TD (P)Tj /T11 1 Tf 30 0 TD (,)Tj /T10 1 Tf 20 0 TD (E)Tj /T11 1 Tf 30 0 TD (\003)Tj /T8 1 Tf 27 4 TD (n)Tj /T11 1 Tf 32 -4 TD [(=)-11000(1)-9000(and)-9000(\003)-9000(i)0(s)-9000(a)-9000(uniformly-)]TJ -593 46 TD (in)Tj 30 0 TD (tegrable)Tj /T9 1 Tf 150 0 TD (G)Tj /T11 1 Tf 25 0 TD [(-martingale,)-16000(con)]TJ 273 0 TD (v)Tj 19 0 TD [(erging)-17000(a.s.)-22000(and)-15000(in)]TJ /T10 1 Tf 318 0 TD (L)Tj /T7 1 Tf 26 4 TD (1)Tj /T11 1 Tf 32 -4 TD [(to)-15000(some)]TJ -873 45 TD (in)Tj 30 0 TD (tegrable)Tj /T9 1 Tf 150 0 TD (G)Tj /T6 1 Tf 23 4 TD (1)Tj /T11 1 Tf 32 -4 TD [(-measurable)-17000(r.v.)-21000(\003)]TJ /T6 1 Tf 321 4 TD (1)Tj /T11 1 Tf 32 -4 TD [(.)-22000(A)-14000(new)-15000(measure)]TJ ET 528.24 596.15 7.2 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 528.24 588.47 Tm (P)Tj /T11 1 Tf 30 0 TD [(,)-15000(ab-)]TJ -926 46 TD [(solutely)-20000(con)]TJ 203 0 TD (tin)Tj 45 0 TD [(uous)-19000(w.r.t.)]TJ /T10 1 Tf 216 0 TD (P)Tj /T11 1 Tf 47 0 TD [(on)-18000(\(\012)]TJ /T10 1 Tf 101 0 TD (;)Tj /T9 1 Tf 17 0 TD (G)Tj /T6 1 Tf 23 4 TD (1)Tj /T11 1 Tf 32 -4 TD [(\),)-18000(can)-18000(b)-1000(e)-18000(obtained)]TJ -684 46 TD (b)Tj 20 0 TD [(y)-22000(de\014ning)-23000(the)-22000(Radon-Nik)]TJ 449 0 TD [(o)-1000(dym)-24000(deriv)]TJ 198 0 TD (ativ)Tj 63 0 TD (e)Tj /T10 1 Tf 40 0 TD (d)Tj ET 502.8 574.31 7.2 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 502.8 566.39 Tm [(P)-5000(=dP)]TJ /T9 1 Tf 99 0 TD (j)Tj /T6 1 Tf 10.001 11 TD (G)Tj /T1 1 Tf 19 4 TD (1)Tj /T11 1 Tf 57 -15 TD (=)Tj -975 45 TD (\003)Tj /T6 1 Tf 27 4 TD (1)Tj /T11 1 Tf 32 -4 TD [(.)-22000(Using)-16000(a)-15000(discrete-time)-16000(v)]TJ 426 0 TD [(ersion)-16000(of)-15000(the)-15000(Cameron-Martin-)]TJ -485 46 TD (Girsano)Tj 128 0 TD [(v)-17000(theorem,)-16000(it)-16000(can)-15000(b)-1000(e)-16000(sho)]TJ 422 0 TD [(wn)-16000(that)-15000(under)]TJ ET 508.08 552.23 7.2 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 508.08 544.55 Tm (P)Tj /T11 1 Tf 29 0 TD (,)Tj /T9 1 Tf 27 0 TD (F)Tj /T8 1 Tf 32 -16 TD (X)Tj /T6 1 Tf -4 23 TD (1)Tj /T11 1 Tf 47 -7 TD (and)Tj /T9 1 Tf -943 46 TD (F)Tj /T8 1 Tf 32 -16 TD (Y)Tj /T6 1 Tf -4 22 TD (1)Tj /T11 1 Tf 44 -6 TD [(are)-12000(indep)-1000(enden)]TJ 250 0 TD (t)Tj /T10 1 Tf 30 0 TD (\033)Tj /T11 1 Tf 23 0 TD (-algebras,)Tj /T10 1 Tf 173 0 TD (Y)Tj /T11 1 Tf 43 0 TD [(is)-13000(an)-12000(i.i.d.)-18000(Gaussian)-14000(pro-)]TJ -590.999 45 TD [(cess)-9000(with)-10000(distribution)]TJ /T10 1 Tf 362 0 TD (N)Tj /T11 1 Tf 35 0 TD (\(0)Tj /T10 1 Tf 34 0 TD (;)Tj /T11 1 Tf 17 0 TD (\006)Tj /T8 1 Tf 28 4 TD (w)Tj /T11 1 Tf 25 -4 TD [(\),)-9000(and)-10000(the)-9000(restrictions)-12000(of)]TJ /T10 1 Tf 403 0 TD (P)Tj /T11 1 Tf 39 0 TD (and)Tj ET 313.2 519.35 7.2 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 313.2 511.67 Tm (P)Tj /T11 1 Tf 42 0 TD [(to)-12000(\(\012)]TJ /T10 1 Tf 89 0 TD (;)Tj /T9 1 Tf 17 0 TD (F)Tj /T8 1 Tf 32 -16 TD (X)Tj /T6 1 Tf -4 23 TD (1)Tj /T11 1 Tf 32 -7 TD [(\))-13000(coincide.)-18000(A)-13000(rev)]TJ 282 0 TD [(erse)-12000(measure)-13000(c)]TJ 241 0 TD [(hange)-14000(can)-13000(b)-1000(e)-12000(ef-)]TJ -730.999 46 TD [(fected)-16000(b)]TJ 135 0 TD [(y)-16000(de\014ning)-17000(similar)-18000(pro)-1000(cesses)]TJ ET 461.04 508.55 5.52 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 461.04 500.63 Tm (\025)Tj /T11 1 Tf 22 0 TD (,)Tj ET 472.8 508.55 6.48 -0.48 re f BT /T11 1 Tf 0.24 0 0 -0.24 472.8 500.63 Tm [(\003,)-16000(with)]TJ ET 507.36 508.55 5.52 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 507.36 500.63 Tm (\025)Tj /T8 1 Tf 22.001 4 TD (n)Tj /T11 1 Tf 36 -4 TD 15 Tc (=1)Tj /T10 1 Tf 64 0 TD 0 Tc (=\025)Tj /T8 1 Tf 41 4 TD (n)Tj /T11 1 Tf 22 -4 TD (,)Tj -994 45 TD [(and)-18000(reco)]TJ 146 0 TD (v)Tj 19 0 TD [(ers)-17000(the)-17000(original)-20000(probabilit)]TJ 437 0 TD [(y)-20000(measure)]TJ /T10 1 Tf 194 0 TD (P)Tj /T11 1 Tf 30 0 TD 29 Tc (.F)Tj 62 0 TD 0 Tc (urther-)Tj -887.999 46 TD [(more,)-17000(conditional)-20000(exp)-1000(ectations)-19000(under)]TJ /T10 1 Tf 650.999 0 TD (P)Tj /T11 1 Tf 47 0 TD (and)Tj ET 499.44 486.47 7.2 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 499.44 478.79 Tm (P)Tj /T11 1 Tf 46 0 TD [(are)-17000(related)]TJ -821.999 46 TD (b)Tj 20 0 TD [(y)-13000(the)-13000(Kallianpu)-1000(r-Strie)-1000(b)-1000(e)0(l)-17000(form)]TJ 510.999 0 TD (ula,)Tj /T10 1 Tf -511.999 96 TD (E)Tj /T9 1 Tf 30 0 TD (f)Tj /T10 1 Tf 19 0 TD (\036)Tj /T11 1 Tf 23 0 TD (\()Tj /T10 1 Tf 15 0 TD (X)Tj /T8 1 Tf 32 4 TD (k)Tj /T11 1 Tf 19 -4 TD (\))Tj /T9 1 Tf 15 0 TD (jF)Tj /T8 1 Tf 43 -18 TD (Y)Tj -4 25 TD (n)Tj /T9 1 Tf 30 -7 TD (g)Tj /T11 1 Tf 30 0 TD (=)Tj ET 389.04 458.39 7.44 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 389.04 450.47 Tm (E)Tj /T9 1 Tf 31 0 TD (f)Tj /T10 1 Tf 19 0 TD (\036)Tj /T11 1 Tf 23 0 TD (\()Tj /T10 1 Tf 15 0 TD (X)Tj /T8 1 Tf 32 4 TD (k)Tj /T11 1 Tf 18 -4 TD (\))Tj ET 425.76 458.39 6.48 -0.48 re f BT /T11 1 Tf 0.24 0 0 -0.24 425.76 450.47 Tm (\003)Tj /T8 1 Tf 27 4 TD (n)Tj /T9 1 Tf 21 -4 TD (jF)Tj /T8 1 Tf 43 -16 TD (Y)Tj -4 22 TD (n)Tj /T9 1 Tf 30 -6 TD (g)Tj ET 389.04 447.11 69.36 -0.48 re f 401.52 445.19 7.44 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 401.52 437.27 Tm (E)Tj /T9 1 Tf 30 0 TD (f)Tj ET 413.28 445.19 6.48 -0.48 re f BT /T11 1 Tf 0.24 0 0 -0.24 413.28 437.27 Tm (\003)Tj /T8 1 Tf 27 4 TD (n)Tj /T9 1 Tf 21 -4 TD (jF)Tj /T8 1 Tf 43 -13 TD (Y)Tj -4 17 TD (n)Tj /T9 1 Tf 30 -4 TD (g)Tj /T6 1 Tf 88 -54 TD (4)Tj /T11 1 Tf -1 23 TD (=)Tj /T10 1 Tf 45 -24 TD (\033)Tj /T8 1 Tf 22 4 TD (n)Tj /T11 1 Tf 21 -4 TD (\()Tj /T10 1 Tf 15 0 TD (\036)Tj /T11 1 Tf 23 0 TD (\()Tj /T10 1 Tf 15 0 TD (X)Tj /T8 1 Tf 32 4 TD (k)Tj /T11 1 Tf 19 -4 TD (\)\))Tj ET 473.04 447.11 42.48 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 483.12 438.47 Tm (\033)Tj /T8 1 Tf 22 4 TD (n)Tj /T11 1 Tf 21 -4 TD (\(1\))Tj 107 -26 TD (:)Tj /T10 1 Tf 22 0 TD (k)Tj /T9 1 Tf 31 0 TD (\024)Tj /T10 1 Tf 41 0 TD (n:)Tj /T11 1 Tf -952 97 TD [(The)-15000(state)-14000(estimation)-17000(problem)-16000(is)-15000(solv)]TJ 619.999 0 TD [(ed)-16000(if)-15000(the)-15000(unnormalized)]TJ -619.999 45 TD (quan)Tj 80 0 TD (tit)Tj 39 0 TD (y)Tj /T10 1 Tf 32 0 TD (\033)Tj /T8 1 Tf 22 4 TD (n)Tj /T11 1 Tf 22 -4 TD (\()Tj /T10 1 Tf 15 0 TD (\036)Tj /T11 1 Tf 23 0 TD (\()Tj /T10 1 Tf 15 0 TD (X)Tj /T8 1 Tf 32 4 TD (k)Tj /T11 1 Tf 18 -4 TD [(\)\))-10000(can)-12000(b)-1000(e)-11000(calculated)-13000(from)-10000(the)-11000(observ)]TJ 594.999 0 TD (ations.)Tj -892.999 46 TD [(Under)-17000(appropriate)-18000(assumptions,)-19000(there)-17000(exist)-17000(forw)]TJ 832 0 TD [(ard,)-17000(bac)]TJ 139 0 TD (k-)Tj -970.999 46 TD (w)Tj 27 0 TD [(ard,)-13000(and)-14000(smo)-1000(othed)-15000(unnormalized)-16000(conditional)-17000(densities)]TJ /T10 1 Tf 923.999 0 TD (\013)Tj /T8 1 Tf 25.001 4 TD (k)Tj /T11 1 Tf 18 -4 TD (,)Tj /T10 1 Tf -994 45 TD (\014)Tj /T8 1 Tf 22 4 TD (k)Tj /T11 1 Tf 19 -4 TD (,)Tj /T10 1 Tf 23 0 TD (\015)Tj /T8 1 Tf 20 4 TD (k)Tj /T11 1 Tf 32 -4 TD (for)Tj /T10 1 Tf 59 0 TD (X)Tj /T8 1 Tf 32 4 TD (k)Tj /T11 1 Tf 31 -4 TD (suc)Tj 52 0 TD [(h)-14000(that)-13000(for)-13000(all)-14000(Borel)-14000(functions)]TJ /T10 1 Tf 498 0 TD (\036)Tj /T11 1 Tf 23 0 TD (\()Tj /T10 1 Tf 15 0 TD (X)Tj /T8 1 Tf 32 4 TD (k)Tj /T11 1 Tf 18 -4 TD (\),)Tj /T10 1 Tf -741 96 TD (\033)Tj /T8 1 Tf 22 4 TD (n)Tj /T11 1 Tf 21 -4 TD (\()Tj /T10 1 Tf 15 0 TD (\036)Tj /T11 1 Tf 23 0 TD (\()Tj /T10 1 Tf 15 0 TD (X)Tj /T8 1 Tf 32 4 TD (k)Tj /T11 1 Tf 18 -4 TD (\)\))Tj 72 0 TD (=)Tj /T5 1 Tf 71 -55 TD (Z)Tj /T10 1 Tf 48 55 TD (\036)Tj /T11 1 Tf 23 0 TD (\()Tj /T10 1 Tf 15 0 TD (x)Tj /T11 1 Tf 22 0 TD (\))Tj /T10 1 Tf 27 0 TD (\015)Tj /T8 1 Tf 20 4 TD (k)Tj /T11 1 Tf 19 -4 TD (\()Tj /T10 1 Tf 15 0 TD (x)Tj /T11 1 Tf 22 0 TD (\))Tj /T10 1 Tf 27 0 TD (dx;)Tj -525 109 TD (\033)Tj /T8 1 Tf 22 4 TD (k)Tj /T11 1 Tf 19 -4 TD (\()Tj /T10 1 Tf 15 0 TD (\036)Tj /T11 1 Tf 23 0 TD (\()Tj /T10 1 Tf 15 0 TD (X)Tj /T8 1 Tf 32 4 TD (k)Tj /T11 1 Tf 18 -4 TD (\)\))Tj 72 0 TD (=)Tj /T5 1 Tf 71 -55 TD (Z)Tj /T10 1 Tf 48 55 TD (\036)Tj /T11 1 Tf 23 0 TD (\()Tj /T10 1 Tf 15 0 TD (x)Tj /T11 1 Tf 22 0 TD (\))Tj /T10 1 Tf 27 0 TD (\013)Tj /T8 1 Tf 25 4 TD (k)Tj /T11 1 Tf 19 -4 TD (\()Tj /T10 1 Tf 15 0 TD (x)Tj /T11 1 Tf 22 0 TD (\))Tj /T10 1 Tf 27 0 TD (dx;)Tj -397 88 TD (\014)Tj /T8 1 Tf 22 4 TD (k)Tj /T11 1 Tf 61 -4 TD (=)Tj ET 414.96 315.11 7.44 -0.48 re f BT /T10 1 Tf 0.24 0 0 -0.24 414.96 307.43 Tm (E)Tj /T9 1 Tf 30 0 TD (f)Tj /T11 1 Tf 19 0 TD (\(\003)Tj /T8 1 Tf 42 4 TD (n)Tj /T10 1 Tf 21 -4 TD (=)Tj /T11 1 Tf 19 0 TD (\003)Tj /T8 1 Tf 27 4 TD (k)Tj /T6 1 Tf 17 0 TD (\000)Tj /T7 1 Tf 24 0 TD (1)Tj /T11 1 Tf 17 -4 TD (\))Tj /T9 1 Tf 15 0 TD 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