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The disorder problem for compound Poisson processes with exponential jumps

By Pavel V. Gapeev


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 Lévy 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

Topics: HA Statistics
Publisher: Institute of Mathematical Statistics
Year: 2005
DOI identifier: 10.1214/105051604000000981
OAI identifier:
Provided by: LSE Research Online

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