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Invariant probability measures for path-dependent regime-switching processes

  • Jianrui Li
  • Jinghai Shao
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Abstract

We consider stochastic functional differential equations with Markovian regime?switching on an (infinitely) countable state space. Via establishing the Feller prop?erty and contraction in L1-Wasserstein distance of the semigroup associated with the segment process, we show the existence and uniqueness of invariant probability measure. In order to cope with switching processes on an infinite state space, we de?velop a truncation method based on a new construction of order preserving coupling for Markov chains to generalize the estimation of exponential functionals for Markov chains with infinite states. The existing sharp estimation is only valid for Markov chains on a finite state space, as it fundamentally relies on the Perron-Frobenius theorem.

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Cite

BibTeXRIS
BibTeX
@misc{li2026invariant,
  title = {{Invariant probability measures for path-dependent regime-switching processes}},
  author = {Jianrui Li and Jinghai Shao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41515},
  eprint = {2610.41515},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41515},
}
RIS
TY  - UNPB
TI  - Invariant probability measures for path-dependent regime-switching processes
AU  - Jianrui Li
AU  - Jinghai Shao
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41515
UR  - https://arxiv.org/abs/2610.41515
AB  - We consider stochastic functional differential equations with Markovian regime?switching on an (infinitely) countable state space. Via establishing the Feller prop?erty and contraction in L1-Wasserstein distance of the semigroup associated with the segment process, we show the existence and uniqueness of invariant probability measure. In order to cope with switching processes on an infinite state space, we de?velop a truncation method based on a new construction of order preserving coupling for Markov chains to generalize the estimation of exponential functionals for Markov chains with infinite states. The existing sharp estimation is only valid for Markov chains on a finite state space, as it fundamentally relies on the Perron-Frobenius theorem.
ER  -