A Note on Exact State Visit Probabilities in Two-State Markov Chains

Fuente: arXiv
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Main Author: Shah, Mohammad Taha
Format: Preprint
Published: 2025
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author Shah, Mohammad Taha
author_facet Shah, Mohammad Taha
contents In this note we derive the exact probability that a specific state in a two-state Markov chain is visited exactly $k$ times after $N$ transitions. We provide a closed-form solution for $\mathbb{P}(N_l = k \mid N)$, considering initial state probabilities and transition dynamics. The solution corrects and extends prior incomplete results, offering a rigorous framework for enumerating state transitions. Numerical simulations validate the derived expressions, demonstrating their applicability in stochastic modeling.
format Preprint
id arxiv_https___arxiv_org_abs_2502_03073
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Note on Exact State Visit Probabilities in Two-State Markov Chains
Shah, Mohammad Taha
Probability
In this note we derive the exact probability that a specific state in a two-state Markov chain is visited exactly $k$ times after $N$ transitions. We provide a closed-form solution for $\mathbb{P}(N_l = k \mid N)$, considering initial state probabilities and transition dynamics. The solution corrects and extends prior incomplete results, offering a rigorous framework for enumerating state transitions. Numerical simulations validate the derived expressions, demonstrating their applicability in stochastic modeling.
title A Note on Exact State Visit Probabilities in Two-State Markov Chains
topic Probability
url https://arxiv.org/abs/2502.03073