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Approximation of the first passage time distribution for the birth-death processes

Aleksejus Kononovicius and Vygintas Gontis

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Abstract: We propose a general method to obtain approximation of the first passage time distribution for the birth-death processes. We rely on the general properties of birth-death processes, Keilson's theorem and the concept of Riemann sum to obtain closed-form expressions. We apply the method to the three selected birth-death processes and the sophisticated order-book model exhibiting long-range memory. We discuss how our approach contributes to the competition between spurious and true long-range memory models.

Date: 2019-02
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Published in Journal of Statistical Mechanics 2019: 073402 (2019)

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