Time Reversal of Diffusions
Haussmann, U. G. ; Pardoux, E.
Ann. Probab., Tome 14 (1986) no. 4, p. 1188-1205 / Harvested from Project Euclid
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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.
Publié le : 1986-10-14
Classification:  Time reversal,  diffusion process,  Markov process,  martingale problem,  Kolmogorov equation,  60J60,  35K15 
@article{1176992362,
     author = {Haussmann, U. G. and Pardoux, E.},
     title = {Time Reversal of Diffusions},
     journal = {Ann. Probab.},
     volume = {14},
     number = {4},
     year = {1986},
     pages = { 1188-1205},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176992362}
}

Haussmann, U. G.; Pardoux, E. Time Reversal of Diffusions. Ann. Probab., Tome 14 (1986) no. 4, pp.  1188-1205. http://gdmltest.u-ga.fr/item/1176992362/