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arXiv · 1902.00924

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

Aleksejus Kononovicius·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.

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Aleksejus Kononovicius, Vygintas Gontis. 2019-02-03. Approximation of the first passage time distribution for the birth-death processes. https://doi.org/10.1088/1742-5468%2Fab2709

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