A Note on Exact State Visit Probabilities in Two-State Markov Chains
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917914375880704 |
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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 |