Properties of perpetual integral functionals of Brownian motion with drift

被引：21
|
作者：
Salminen, P [1 ]
Yor, M
机构：
[1] Abo Akad Univ, Dept Math, SF-20500 Turku, Finland
[2] Univ Paris 06, Lab Probabil, F-75252 Paris, France
来源：
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2005年 / 41卷 / 03期
关键词：
local time; Green function; Kac's moment formula; khas'minskii's lemma; last exit time;
D O I：
10.1016/j.anihpb.2004.01.006
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In this paper we study integrability properties of the random variable I infinity(f) := integral(infinity)(0) f (B-t((mu)))dt, where {B-t((mu)): t >= 0} is a Brownian motion with drift mu > 0 and f is a non-negative, Borel measurable function. In particular, we find conditions under which I infinity (f) (i) is finite a.s., (ii) has all the moments, (iii) has some exponential moments, and (iv) has bounded potential. (c) 2005 Elsevier SAS. All rights reserved.
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页码：335 / 347
页数：13
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