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Periodic measures for time-inhomogeneous stochastic differential equations driven by multiplicative α-stable processes: Existence, uniqueness and numerical approximation

  • Jiaquan Lu
  • Huaizhong Zhao
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Abstract

In this paper, we study the periodic measures within the context of time-inhomogeneous Markov processes. By extending the Hairer--Mattingly method to the time-inhomogeneous case, we first establish the existence, uniqueness and exponential ergodicity of periodic measures for general time-periodic Markov processes. These results are subsequently applied to time-inhomogeneous stochastic differential equations under the assumption that the drift is weakly dissipative and locally Lipschitz. We further employ the truncated Euler--Maruyama scheme to study numerical approximations of the periodic measures and derive the convergence rate between the exact and discrete periodic measures. These numerical results are new even in the time-homogeneous case under the assumptions considered in this paper.

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Cite

BibTeXRIS
BibTeX
@misc{lu2026periodic,
  title = {{Periodic measures for time-inhomogeneous stochastic differential equations driven by multiplicative $α$-stable processes: Existence, uniqueness and numerical approximation}},
  author = {Jiaquan Lu and Huaizhong Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35519},
  eprint = {2610.35519},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35519},
}
RIS
TY  - UNPB
TI  - Periodic measures for time-inhomogeneous stochastic differential equations driven by multiplicative α-stable processes: Existence, uniqueness and numerical approximation
AU  - Jiaquan Lu
AU  - Huaizhong Zhao
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35519
UR  - https://arxiv.org/abs/2610.35519
AB  - In this paper, we study the periodic measures within the context of time-inhomogeneous Markov processes. By extending the Hairer--Mattingly method to the time-inhomogeneous case, we first establish the existence, uniqueness and exponential ergodicity of periodic measures for general time-periodic Markov processes. These results are subsequently applied to time-inhomogeneous stochastic differential equations under the assumption that the drift is weakly dissipative and locally Lipschitz. We further employ the truncated Euler--Maruyama scheme to study numerical approximations of the periodic measures and derive the convergence rate between the exact and discrete periodic measures. These numerical results are new even in the time-homogeneous case under the assumptions considered in this paper.
ER  -