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arXiv · 1803.09801

On approximations for the distribution of the time of first level crossing

Vsevolod Malinovskii
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Abstract

This paper is an overview of the classical level crossing problem which is studied extensively in the literature and is fundamental in many branches of applied probability. We discuss a number of approximations with an emphasis on their performance, methods of justification and technical conditions which are required in these methods, including a new approximation called "inverse Gaussian". It is derived by a new method, is fruitful for solving related problems, and is valid under mild regularity conditions. We emphasize its novelty and boons.

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Vsevolod Malinovskii. 2018-03-26. On approximations for the distribution of the time of first level crossing. https://arxiv.org/abs/1803.09801

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