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

2018/03/26 by V. K. Malinovskiǐ, Vsevolod Malinovskii, Malinovskii, Vsevolod
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Scientific Research and Discoveries #Statistical Distribution Estimation and Applications #math.PR

paper · pdf · doi:10.48550/arxiv.1803.09801

arxiv created 2018/03/26 · openalex publication_date 2018/03/26 · arxiv updated 2018/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Convergence of Random Processes and Limit Theorems in Probability Theory
• Generalized inverse Gaussian distributions and the time of first level crossing
• On approximations for the distribution of first level crossing time

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• On the time of first level crossing and inverse Gaussian distribution
• On approximations for the distribution of first level crossing time
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