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Ergodicity of stochastic functional differential equation with jumps and finite delay
Abstract
This paper investigates the ergodicity of stochastic functional differential equations with jumps under the Wasserstein distance by the generalized coupling method. Two key conditions are verified. The first is verified by establishing an exponential decay bound for the coupled segment processes and applying the Girsanov theorem for Itô-Lévy processes. The second is verified through a support theorem developed for an auxiliary process and then extended to the underlying process. Combining these results yields the desired ergodicity.
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BibTeX
@misc{ye2026ergodicity,
title = {{Ergodicity of stochastic functional differential equation with jumps and finite delay}},
author = {Mingkun Ye and Yafei Zhai and Zuozheng Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.04684},
eprint = {2605.04684},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.04684},
}
RIS
TY - UNPB
TI - Ergodicity of stochastic functional differential equation with jumps and finite delay
AU - Mingkun Ye
AU - Yafei Zhai
AU - Zuozheng Zhang
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2605.04684
UR - https://arxiv.org/abs/2605.04684
AB - This paper investigates the ergodicity of stochastic functional differential equations with jumps under the Wasserstein distance by the generalized coupling method. Two key conditions are verified. The first is verified by establishing an exponential decay bound for the coupled segment processes and applying the Girsanov theorem for Itô-Lévy processes. The second is verified through a support theorem developed for an auxiliary process and then extended to the underlying process. Combining these results yields the desired ergodicity.
ER -