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<p>The study aims to investigate the weak convergence of nearestneighbor random walks in one-dimensional space, with the assumption that thetransition probabilities tend towards a constant within the range <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10474_2024_1497_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">\([ 0, 1/2 ]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation>. Thepaper will demonstrate limit theorems based on the bias or balance of the randomwalk, utilizing the method of moments.</p>

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On the convergence of random walks in one-dimensional space

  • 期刊论文

  • 发表日期：

    2025年1月18日

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  • T.-B.-B Duong,
  • H. -C Lam

摘要

The study aims to investigate the weak convergence of nearestneighbor random walks in one-dimensional space, with the assumption that thetransition probabilities tend towards a constant within the range \([ 0, 1/2 ]\) [ 0 , 1 / 2 ] . Thepaper will demonstrate limit theorems based on the bias or balance of the randomwalk, utilizing the method of moments.