QUASI-STATIONARY DISTRIBUTIONS FOR A BROWNIAN-MOTION WITH DRIFT AND ASSOCIATED LIMIT LAWS

被引:37
作者
MARTINEZ, S
SANMARTIN, J
机构
关键词
BROWNIAN MOTION WITH DRIFT; QUASI-STATIONARY DISTRIBUTIONS;
D O I
10.2307/3215316
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
We prove that the quasi-invariant measures associated to a Brownian motion with negative drift X form a one-parameter family. The minimal one is a probability measure inducing the transition density of a three-dimensional Bessel process, and it is shown that it is the density of the limit distribution lim(t-->infinity)P(x)(X is an element of A\tau(0)(X) > t). It is also shown that the minimal quasi-invariant measure of infinite mass induces the density of the limit distribution lim(M-->infinity)P(x)(X is an element of A\tau(0)(X) > tau(M)(X)) which is the law of a Bessel process with drift.
引用
收藏
页码:911 / 920
页数:10
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