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On a piece-wise deterministic Markov process model

✍ Scribed by K. Borovkov; A. Novikov

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
101 KB
Volume
53
Category
Article
ISSN
0167-7152

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✦ Synopsis

We study a piece-wise deterministic Markov process having jumps of i.i.d. sizes with a constant intensity and decaying at a constant rate (a special case of a storage process with a general release rule). Necessary and su cient conditions for the process to be ergodic are found, its stationary distribution is found in explicit form. Further, the Laplace transform of the ΓΏrst crossing time of a ΓΏxed barrier by the process is shown to satisfy a Fredholm equation of second kind. Solution to this equation is given by exponentially fast converging Neumann series; convergence rate of the series is estimated. Our results can be applied to an important reliability problem.

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