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Finite-State Time-Inhomogeneous Markov Chains Conditioned to Survive

  • Kohki Iba
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Abstract

We study conditioning on long survival for time-inhomogeneous Markov chains on finite state spaces. We assume that a sequence of substochastic transition kernels converges to an irreducible substochastic kernel and that the transition probabilities admit asymptotic expansions up to order n−2. Under these assumptions, we construct a positive space-time harmonic function and prove that the limiting path distributions under conditioning on long survival are given by the corresponding Doob h-transform. We also investigate the long-time behavior of the resulting conditioned process. Finally, we apply our general theory to an elephant random walk, a generalized Pólya urn model, time-inhomogeneous Wright--Fisher and Moran models, and noncolliding random walks.

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Cite

BibTeXRIS
BibTeX
@misc{iba2026finitestate,
  title = {{Finite-State Time-Inhomogeneous Markov Chains Conditioned to Survive}},
  author = {Kohki Iba},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38590},
  eprint = {2610.38590},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38590},
}
RIS
TY  - UNPB
TI  - Finite-State Time-Inhomogeneous Markov Chains Conditioned to Survive
AU  - Kohki Iba
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38590
UR  - https://arxiv.org/abs/2610.38590
AB  - We study conditioning on long survival for time-inhomogeneous Markov chains on finite state spaces. We assume that a sequence of substochastic transition kernels converges to an irreducible substochastic kernel and that the transition probabilities admit asymptotic expansions up to order n^−2. Under these assumptions, we construct a positive space-time harmonic function and prove that the limiting path distributions under conditioning on long survival are given by the corresponding Doob h-transform. We also investigate the long-time behavior of the resulting conditioned process. Finally, we apply our general theory to an elephant random walk, a generalized Pólya urn model, time-inhomogeneous Wright--Fisher and Moran models, and noncolliding random walks.
ER  -