THE 1ST-PASSAGE DENSITY OF THE BROWNIAN-MOTION PROCESS TO A CURVED BOUNDARY

被引：73

作者：

DURBIN, J ^{[1
]}

WILLIAMS, D ^{[1
]}

机构：

[1] UNIV CALIF SANTA BARBARA,STAT & APPL PROBABIL PROGRAM,SANTA BARBARA,CA 93106

来源：

JOURNAL OF APPLIED PROBABILITY | 1992年 / 29卷 / 02期

关键词：

BROWNIAN BRIDGE; CONTINUOUS GAUSS-MARKOV PROCESS; BOUNDARY-CROSSING;

D O I：

10.2307/3214567

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：

An expression for the first-passage density of Brownian motion to a curved boundary is expanded as a series of multiple integrals. Bounds are given for the error due to truncation of the series when the boundary is wholly concave or wholly convex. Extensions to the Brownian bridge and to continuous Gauss-Markov processes are given. The series provides a practical method for calculating the probability that a sample path crosses the boundary in a specified time-interval to a high degree of accuracy. A numerical example is given.

引用

页码：291 / 304

页数：14

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