Asymptotic Bismut formulae for stochastic functional differential equations with infinite delay
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- by Ya Wang, Fuke Wu and George Yin
- Proc. Amer. Math. Soc. 150 (2022), 4037-4051
- DOI: https://doi.org/10.1090/proc/15966
- Published electronically: April 15, 2022
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Abstract:
Using Malliavin calculus, this paper establishes asymptotic Bismut formulae for stochastic functional differential equations with infinite delay. Both nondegenerate and degenerate diffusion coefficients are treated. In addition, combined with the corresponding exponential ergodicity, stabilization bounds for $\nabla P_{t}f$ as $t\rightarrow \infty$ are derived.References
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Bibliographic Information
- Ya Wang
- Affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, People’s Republic of China
- Email: y_wang@hust.edu.cn
- Fuke Wu
- Affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, People’s Republic of China
- Email: wufuke@hust.edu.cn
- George Yin
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269-1009
- MR Author ID: 248052
- ORCID: 0000-0002-2951-0704
- Email: gyin@uconn.edu
- Received by editor(s): June 13, 2021
- Received by editor(s) in revised form: December 9, 2021
- Published electronically: April 15, 2022
- Additional Notes: The first and second authors were supported in part by the National Natural Science Foundation of China (Grant Nos. 61873320). The third author was supported in part by the National Science Foundation under grant DMS-2114649
- Communicated by: Zhen-Qing Chen
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 4037-4051
- MSC (2020): Primary 60J60, 34K50
- DOI: https://doi.org/10.1090/proc/15966
- MathSciNet review: 4446250