Backward Nonlinear Smoothing Diffusions

Anderson, BDO; Bishop, AN; Moral, PD; Palmier, C

Backward Nonlinear Smoothing Diffusions

Anderson, BDO Bishop, AN Moral, PD Palmier, C

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Publisher:: Society for Industrial and Applied Mathematics
Publication Type:: Journal Article
Citation:: Theory of Probability and Its Applications, 2019, 66, (2), pp. 235-262
Issue Date:: 2019-11-01

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Field	Value	Language
dc.contributor.author	Anderson, BDO
dc.contributor.author	Bishop, AN
dc.contributor.author	Moral, PD
dc.contributor.author	Palmier, C
dc.date.accessioned	2022-04-30T22:47:30Z
dc.date.available	2022-04-30T22:47:30Z
dc.date.issued	2019-11-01
dc.identifier.citation	Theory of Probability and Its Applications, 2019, 66, (2), pp. 235-262
dc.identifier.issn	0040-585X
dc.identifier.issn	1095-7219
dc.identifier.uri	http://hdl.handle.net/10453/156865
dc.description.abstract	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 later 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.
dc.language	en
dc.publisher	Society for Industrial and Applied Mathematics
dc.relation.ispartof	Theory of Probability and Its Applications
dc.relation.isbasedon	10.1137/S0040585X97T99037X
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	0104 Statistics
dc.subject.classification	Statistics & Probability
dc.title	Backward Nonlinear Smoothing Diffusions
dc.type	Journal Article
utslib.citation.volume	66
utslib.for	0104 Statistics
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - CHT - Health Technologies
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Biomedical Engineering
pubs.organisational-group	/University of Technology Sydney/Centre for Health Technologies (CHT)
utslib.copyright.status	open_access	*
pubs.consider-herdc	false
dc.date.updated	2022-04-30T22:47:28Z
pubs.issue	2
pubs.publication-status	Published
pubs.volume	66
utslib.citation.issue	2

Abstract:

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 later 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.

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http://hdl.handle.net/10453/156865