TY - JOUR

T1 - Fixed-Point smoothing of scalar diffusions 1

T2 - an asymptotically optimal smoother

AU - Steinberg, Y.

AU - Bobrovsky, B. Z.

AU - Schuss, Z.

PY - 1994

Y1 - 1994

N2 - The problem of nonlinear estimation of the initial value of a given diffusion process, given its noisy measurements as a function of time, is the fixed-point smoothing problem. A Zakai-type equation is derived for the time evolution of an unnormalized version of the conditional probability density function (cpdf) of the initial value, given the measurements up to time t. The equation for the cpdf of the initial value is coupled to a Zakai equation for the filtering problem with a singular initial condition.

AB - The problem of nonlinear estimation of the initial value of a given diffusion process, given its noisy measurements as a function of time, is the fixed-point smoothing problem. A Zakai-type equation is derived for the time evolution of an unnormalized version of the conditional probability density function (cpdf) of the initial value, given the measurements up to time t. The equation for the cpdf of the initial value is coupled to a Zakai equation for the filtering problem with a singular initial condition.

UR - http://www.scopus.com/inward/record.url?scp=0028444760&partnerID=8YFLogxK

U2 - 10.1137/S0036139990188904

DO - 10.1137/S0036139990188904

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AN - SCOPUS:0028444760

SN - 0036-1399

VL - 54

SP - 833

EP - 853

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 3

ER -