The mean velocity of a Brownian motion in a random Levy potential

• 成果类型: Article
• 署名作者: Carmona, P
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1023481110
• 发表日期: 1997
• 页码: 1774-1788
• 关键词: random environment; limit; DIFFUSIONS; LAW

摘要

Brownian motion in a random Levy potential V is the informal solution of the stochastic differential equation dX(t) = dB(t) - 1/2V' (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 Levy exponent phi of V, defined by E[e(mV(t))] = e(-t phi(m)).