The influence of a power law drift on the exit time of Brownian motion from a half-line

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:117

Article

DeBlassie, Dante ; Smits, Robert

关键词: lifetime;    Brownian motion;    Bessel process;    large deviations;    calculus of variations;    h-transform;   

DOI  :  10.1016/j.spa.2006.09.009

来源: Elsevier

【 摘 要 】

The addition of a Bessel drift 1/x to a Brownian motion affects the lifetime of the process in the interval (0, infinity) in a well-understood way. We study the corresponding effect of a power -beta/x(p) (beta not equal 0, p > 0) of the Bessel drift. The most interesting case occurs when beta > 0. If p > 1 then the effect of the drift is not too great in the sense that the exit time has the same critical value q(0) for the existence of qth moments (q > 0) as the exit time of Brownian motion. When p < 1, the influence is much greater: the exit time has exponential moments. (c) 2006 Elsevier B.V. All rights reserved.

【 授权许可】

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