A Local Limit Theorem for the Minimum of a Random Walk with Markovian Increments

Yinna Ye

doi:10.3969/j.issn.1001-4268.2016.01.002

A Local Limit Theorem for the Minimum of a Random Walk with Markovian Increments

Yinna Ye

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The local limit theorems for the minimum of a random walk with Markovian increment is given, with using Presman's factorization theory. This result implies the asymptotic behaviour of the survival probability for a critical branching process in Markovian dependent random environment.

Original language	English
Pages (from-to)	23-50
Number of pages	28
Journal	Chinese Journal of Applied Probability and Statistics
Volume	32
Issue number	1
DOIs	https://doi.org/10.3969/j.issn.1001-4268.2016.01.002
Publication status	Published - Feb 2016

Keywords

Local Limit Theorem
Markov chain
semi-Markov Chain
Random walk

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10.3969/j.issn.1001-4268.2016.01.002Licence: CC BY-NC-ND

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title = "A Local Limit Theorem for the Minimum of a Random Walk with Markovian Increments",

abstract = "The local limit theorems for the minimum of a random walk with Markovian increment is given, with using Presman's factorization theory. This result implies the asymptotic behaviour of the survival probability for a critical branching process in Markovian dependent random environment.",

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KW - Markov chain

KW - semi-Markov Chain

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JO - Chinese Journal of Applied Probability and Statistics

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A Local Limit Theorem for the Minimum of a Random Walk with Markovian Increments

Abstract

Keywords

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