整数值随机游动边界交叉问题的精确公式

IF 0.8 3区数学 Q2 MATHEMATICS

Izvestiya Mathematics Pub Date : 2023-01-01 DOI:10.4213/im9323e

V. I. Lotov

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引用次数: 1

摘要

对于一类广泛的整数值随机游动，我们得到了第一个超水平的分布和相应的更新函数的精确表达式，以及轨迹极限的分布。讨论了在条形边界处具有切换的随机漫步的预平稳分布和平稳分布的显式表达式的可能性。该研究是基于所研究分布的双矩生成函数的分解表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Exact formulas in some boundary crossing problems for integer-valued random walks

For a wide class of integer-valued random walks, we obtain exact expressions for the distribution of the first excess over level and the corresponding renewal function as well as for the distribution of the trajectory supremum if it is finite. We discuss possibilities of obtaining explicit expressions for pre-stationary and stationary distributions of a random walk with switchings at the strip boundaries. The research is based on the factorization representations for the double moment generating functions of the distributions under study.

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来源期刊

Izvestiya Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. This publication covers all fields of mathematics, but special attention is given to: Algebra; Mathematical logic; Number theory; Mathematical analysis; Geometry; Topology; Differential equations.