On the existence of a time inhomogeneous skew Brownian motion and some related laws

被引：19
作者：
Etore, Pierre [1 ]
Martinez, Miguel [1 ]
机构：
[1] Univ Paris Est Marne la Vallee, Paris, France
来源：
ELECTRONIC JOURNAL OF PROBABILITY | 2012年 / 17卷
关键词：
Skew Brownian motion; Local time; Straddling excursion; LOCAL TIME; EQUATION; FLOW;
D O I：
10.1214/EJP.v17-1858
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：
This article is devoted to the construction of a solution for the "skew inhomogeneous Brownian motion" equation: B-t(beta) = x + W-t + integral(t)(0) beta(s)dL(s)(0)(B-beta), t >= 0. Here beta : R+ -> [-1, 1] is a Borel function, W is a standard Brownian motion, and L-t(0) (B-beta) stands for the symmetric local time at 0 of the unknown process B-beta. Using the description of the straddling excursion above a deterministic time t, we also compute the joint law of (B-t(beta), L-t(0), (B-beta), G(t)(beta)) where G(t)(beta) is the last passage time at 0 before t of B-beta.
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页数：27
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