The Annals of Probability

Time Reversal of Diffusions

U. G. Haussmann and E. Pardoux

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Abstract

It is shown that if a diffusion process, $\{X_t: 0 \leq t \leq 1\}$, on $R^d$ satisfies $dX_t = b(t, X_t) dt + \sigma (t, X_t) dw_t$ then the reversed process, $\{\bar{X}_t: 0 \leq t \leq 1\}$ where $\bar{X}_t = X_{1 - t}$, is again a diffusion with drift $\bar{b}$ and diffusion coefficient $\bar{\sigma}$, provided some mild conditions on $b, \sigma$, and $p_0$, the density of the law of $X_0$, hold. Moreover $\bar{b}$ and $\bar\sigma$ are identified.

Article information

Source
Ann. Probab., Volume 14, Number 4 (1986), 1188-1205.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992362

Digital Object Identifier
doi:10.1214/aop/1176992362

Mathematical Reviews number (MathSciNet)
MR866342

Zentralblatt MATH identifier
0607.60065

JSTOR
links.jstor.org

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 35K15: Initial value problems for second-order parabolic equations

Keywords
Time reversal diffusion process Markov process martingale problem Kolmogorov equation

Citation

Haussmann, U. G.; Pardoux, E. Time Reversal of Diffusions. Ann. Probab. 14 (1986), no. 4, 1188--1205. doi:10.1214/aop/1176992362. https://projecteuclid.org/euclid.aop/1176992362


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