Linear Algebra-Based Solution of Trinomial Markov Chain-Random Walk Between an Absorbing and an Elastic Barrier - Elshehawey, Ahmed; Zayed, Mohammad; Abdelsamiea, Abdelsamiea; Ibrahim, Mohamed; Aboalkhair, Ahmad (Statistics, Optimization & Information Computing, 2025)
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.