Linear Algebra-Based Solution of Trinomial Markov Chain-Random Walk Between an Absorbing and an Elastic Barrier

  • A. M. Elshehawey Department of Applied, Mathematical & Actuarial Statistics, Faculty of Commerce, Damietta University, New Damietta 34519
  • Mohammad A. Zayed Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Saudi Arabia
  • Abdelsamiea Tahsin Abdelsamiea Department of Economics, College of Business, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
  • Mohamed Ibrahim Department of Quantitative Methods, College of Business, King Faisal University, Saudi Arabia
  • Ahmad M. Aboalkhair Department of Applied Statistics and Insurance, Faculty of Commerce, Mansoura University, Egypt; Department of Quantitative Methods, College of Business, King Faisal University, Saudi Arabia
DOI: https://doi.org/10.19139/soic-2310-5070-2806
Keywords: Markov chain-random walk; elastic barrier; eigenvalues and eigenvectors

Abstract

Two trinomial Markov chain-random walk (MC-RW) problems involving nonnegative integers amidst an elastic and an absorbing barrier are considered. The first has an elastic barrier at the origin and an absorber barrier at the end-state N, while the second is the opposite. Employing an unconventional approach based on eigenvalues and eigenvectors, we derive explicit formulas for the probabilities of absorption, segregation, and annihilation at the barriers. We also extract simple closed-form expressions for specific scenarios, including the semi-infinite lattice segment case.
Published
2025-09-06
How to Cite
Elshehawey, A., Zayed, M., Abdelsamiea, A., Ibrahim, M., & Aboalkhair, A. (2025). Linear Algebra-Based Solution of Trinomial Markov Chain-Random Walk Between an Absorbing and an Elastic Barrier. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2806
Issue
Online First
Section
Research Articles
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