Asymptotic Theorems for Discrete Markov Chains

Halidias, Nikolaos (2024) Asymptotic Theorems for Discrete Markov Chains. Asian Journal of Probability and Statistics, 26 (2). pp. 1-17. ISSN 2582-0230

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Let Xₙ be a discrete time Markov chain with state space S(countably infinite, in general) and initial probability distribution μ⁽⁰⁾= (P(X₀=i1),P(X₀=i2),···,). Can we compute or at least estimate the probabilities P(Xₙ=j|X₀=i) and P(Xₙ=j) for largen? We will discuss this question and give some answers even if there exists periodic states. We will also relate the limiting probabilities with the ergodic type of limits and prove that the computation of the limiting probabilities are a stronger result than that of the ergodic theorem. Finally, we will mention some open problems regarding these limiting probabilities.

Item Type: Article
Subjects: Eurolib Press > Mathematical Science
Depositing User: Managing Editor
Date Deposited: 10 Feb 2024 06:25
Last Modified: 10 Feb 2024 11:20

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