ANDERSON, Brian; BISHOP, Adrian; DEL MORAL, Pierre; PALMIER, Camille

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ANDERSON, Brian
Australian National University [ANU]
Commonwealth Scientific and Industrial Research Organisation [Australia] [CSIRO]

BISHOP, Adrian
University of Technology Sydney [UTS]

DEL MORAL, Pierre
Quality control and dynamic reliability [CQFD]

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2019-10-31

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We present a backward diffusion flow (i.e. a backward-in-time stochastic differential equation) whose marginal distribution at any (earlier) time is equal to the smoothing distribution when the terminal state (at a latter time) is distributed according to the filtering distribution. This is a novel interpretation of the smoothing solution in terms of a nonlinear diffusion (stochastic) flow. This solution contrasts with, and complements, the (backward) deterministic flow of probability distributions (viz. a type of Kushner smoothing equation) studied in a number of prior works. A number of corollaries of our main result are given including a derivation of the time-reversal of a stochastic differential equation, and an immediate derivation of the classical Rauch-Tung-Striebel smoothing equations in the linear setting.< Leer menos

Palabras clave en inglés

Nonlinear filtering and smoothing

Kalman-Bucy filter

Rauch-Tung-Striebel smoother

Particle filtering and smoothing

Diffusion equations

Stochastic semigroups

Backward stochastic integration

Backward Itô-Ventzell formula

Tme-reversed stochastic differential equations

Zakai and Kushner-Stratonovich equations

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Backward Nonlinear Smoothing Diffusions

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