| Autor: |
Anderson, Brian D. O., Bishop, Adrian N., Del Moral, Pierre, Palmier, Camille |
| Rok vydání: |
2019 |
| Předmět: |
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| Zdroj: |
Theory of Probability & Its Applications, Volume 66, Issue 2, pages: 245-262, 2021 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1137/S0040585X97T99037X |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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