The mean velocity of a Brownian motion in a random Lévy potential
Carmona, Philippe
Ann. Probab., Tome 25 (1997) no. 4, p. 1774-1788 / Harvested from Project Euclid
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A Brownian motion in a random Lévy potential V is the informal solution of the stochastic differential equation $$dX_t = dB_t - 1/2 V'(X_t)dt,$$ where $B$ is a Brownian motion independent of $V$. ¶ We generalize some results of Kawazu-Tanaka, who considered for $V$ a Brownian motion with drift, by proving that $X_t /t$ converges almost surely to a constant, the mean velocity, which we compute in terms of the Lévy exponent $\phi$ of $V$, defined by $\mathbb{E}[e^{mV(t)}]=e{-t\phi(m)}$.
Publié le : 1997-10-14
Classification:  Diffusion process,  random walk,  random media,  60J60,  60J30,  60J15,  60J65 
@article{1023481110,
     author = {Carmona, Philippe},
     title = {The mean velocity of a Brownian motion in a random L\'evy
		 potential},
     journal = {Ann. Probab.},
     volume = {25},
     number = {4},
     year = {1997},
     pages = { 1774-1788},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1023481110}
}

Carmona, Philippe. The mean velocity of a Brownian motion in a random Lévy
		 potential. Ann. Probab., Tome 25 (1997) no. 4, pp.  1774-1788. http://gdmltest.u-ga.fr/item/1023481110/