Backward Nonlinear Smoothing Diffusions
| hal.structure.identifier | Australian National University [ANU] | |
| hal.structure.identifier | Commonwealth Scientific and Industrial Research Organisation [Canberra] [CSIRO] | |
| dc.contributor.author | ANDERSON, Brian | |
| hal.structure.identifier | University of Technology Sydney [UTS] | |
| dc.contributor.author | BISHOP, Adrian | |
| hal.structure.identifier | Quality control and dynamic reliability [CQFD] | |
| dc.contributor.author | DEL MORAL, Pierre | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PALMIER, Camille | |
| dc.date.accessioned | 2024-04-04T02:59:21Z | |
| dc.date.available | 2024-04-04T02:59:21Z | |
| dc.date.issued | 2019-10-31 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192736 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.subject.en | Nonlinear filtering and smoothing | |
| dc.subject.en | Kalman-Bucy filter | |
| dc.subject.en | Rauch-Tung-Striebel smoother | |
| dc.subject.en | Particle filtering and smoothing | |
| dc.subject.en | Diffusion equations | |
| dc.subject.en | Stochastic semigroups | |
| dc.subject.en | Backward stochastic integration | |
| dc.subject.en | Backward Itô-Ventzell formula | |
| dc.subject.en | Tme-reversed stochastic differential equations | |
| dc.subject.en | Zakai and Kushner-Stratonovich equations | |
| dc.title.en | Backward Nonlinear Smoothing Diffusions | |
| dc.type | Rapport | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.subject.hal | Mathématiques [math]/Optimisation et contrôle [math.OC] | |
| dc.identifier.arxiv | 1910.14511 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.type.institution | ANU; UTS; INRIA; IMB. | |
| bordeaux.type.report | rr | |
| hal.identifier | hal-02342600 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02342600v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2019-10-31&rft.au=ANDERSON,%20Brian&BISHOP,%20Adrian&DEL%20MORAL,%20Pierre&PALMIER,%20Camille&rft.genre=unknown |
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