The disorder problem for compound Poisson processes with exponential jumps

被引：20

作者：

Gapeev, PV ^{[1
]}

机构：

[1] Russian Acad Sci, Inst Control Sci, Moscow 117997, Russia

来源：

ANNALS OF APPLIED PROBABILITY | 2005年 / 15卷 / 1A期

关键词：

disorder (quickest detection) problem; Levy process; compound Poisson process; optimal stopping; integro-differential free-boundary problem; principles of smooth and continuous fit; measure of jumps and its compensator; Girsanov's theorem for semi martingales; Ito's formula;

D O I：

10.1214/105051604000000981

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：

The problem of disorder seeks to determine a stopping time which is as close as possible to the unknown time of "disorder" when the observed process changes its probability characteristics. We give a partial answer to this question for some special cases of Levy processes and present a complete solution of the Bayesian and variational problem for a compound Poisson process with exponential jumps. The method of proof is based on reducing the Bayesian problem to an integro-differential free-boundary problem where, in some cases, the smooth-fit principle breaks down and is replaced by the principle of continuous fit.

引用

页码：487 / 499

页数：13

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