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This paper focuses on two-time-scale coupled stochastic functional differential equations (SFDEs). The system under consideration has a slow component and a fast component. Both components depend on the segment process (an infinite dimension process) of the slow component. To overcome the difficulty due to the past dependence and the coupling of the segment process, such properties as the H\"{o}lder continuity and tightness on a space of continuous functions are investigated first for the segment process. In addition, it is also shown that the solution of a fixed-x equation depends continuously on the parameters. Then using the martingale problem formulation, an average principle is established by a direct averaging.
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Rate of homogenization for fully-coupled McKean–Vlasov SDEs
In this paper, we consider a fully-coupled slow–fast system of McKean–Vlasov stochastic differential equations with full dependence on the slow and fast component and on the law of the slow component and derive convergence rates to its homogenized limit. We do not make periodicity assumptions, but we impose conditions on the fast motion to guarantee ergodicity. In the course of the proof we obtain related ergodic theorems and we gain results on the regularity of Poisson type of equations and of the associated Cauchy problem on the Wasserstein space that are of independent interest.
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- Award ID(s):
- 2107856
- PAR ID:
- 10404919
- Date Published:
- Journal Name:
- Stochastics and Dynamics
- ISSN:
- 0219-4937
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1142/S0219493723500132
