On approximations for the distribution of first level crossing time

Vsevolod K. Malinovskii; Konstantin V. Malinovskii

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arXiv · 1708.08678

On approximations for the distribution of first level crossing time

Vsevolod K. Malinovskii·Konstantin V. Malinovskii

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Abstract

We investigate performance of approximations put forth in \citeNP{[Malinovskii 2017a]} and \citeNP{[Malinovskii 2017b]} for the distribution of the time of first level $u$ crossing by the random process $\homV{s}-cs$, $s>0$, where $\homV{s}$ is compound renewal process. In the case of Exponential inter-renewal and jump size random variables, we compare the approximations with exact and with simulation results. In a few other cases including Erlang and Pareto inter-renewal and jump size random variables, where exact results are absent, we compare the approximations with simulation results.

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Vsevolod K. Malinovskii, Konstantin V. Malinovskii. 2017-08-29. On approximations for the distribution of first level crossing time. https://arxiv.org/abs/1708.08678

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