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October, 1986 Time Reversal of Diffusions
U. G. Haussmann, E. Pardoux
Ann. Probab. 14(4): 1188-1205 (October, 1986). DOI: 10.1214/aop/1176992362


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.


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U. G. Haussmann. E. Pardoux. "Time Reversal of Diffusions." Ann. Probab. 14 (4) 1188 - 1205, October, 1986.


Published: October, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0607.60065
MathSciNet: MR866342
Digital Object Identifier: 10.1214/aop/1176992362

Primary: 60J60
Secondary: 35K15

Keywords: diffusion process , Kolmogorov equation , Markov process , Martingale problem , Time reversal

Rights: Copyright © 1986 Institute of Mathematical Statistics

Vol.14 • No. 4 • October, 1986
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