Entrance measures and dynamics for time-inhomogeneous McKean-Vlasov stochastic differential equations
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| Format: | Preprint |
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2026
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| _version_ | 1866908983178035200 |
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| author | Feng, Chunrong Qu, Baoyou Zhao, Huaizhong |
| author_facet | Feng, Chunrong Qu, Baoyou Zhao, Huaizhong |
| contents | In this paper, we study the entrance measures of time-inhomogeneous McKean-Vlasov SDEs. The existence is obtained in great generality, where the system can be expanding globally and/or degenerate for numerous number of time intervals. When the parameters are periodic/quasi-periodic in time, we obtain the existence of periodic/asymptotic quasi-periodic measures. In this case, a double-lift of the random dynamical system first to a dynamical system on cylinder and then on the graph of reparameterized process living on the cylinder is introduced. The double-lifted system gives to a continuous dynamical system over probability measures on the cylinder, and the lifted multi-parameter measure of the asymptotic quasi-periodic measure can then lead to an invariant measure of the lifted semigroup. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_19187 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Entrance measures and dynamics for time-inhomogeneous McKean-Vlasov stochastic differential equations Feng, Chunrong Qu, Baoyou Zhao, Huaizhong Probability 60H10, 60B10, 37A50 In this paper, we study the entrance measures of time-inhomogeneous McKean-Vlasov SDEs. The existence is obtained in great generality, where the system can be expanding globally and/or degenerate for numerous number of time intervals. When the parameters are periodic/quasi-periodic in time, we obtain the existence of periodic/asymptotic quasi-periodic measures. In this case, a double-lift of the random dynamical system first to a dynamical system on cylinder and then on the graph of reparameterized process living on the cylinder is introduced. The double-lifted system gives to a continuous dynamical system over probability measures on the cylinder, and the lifted multi-parameter measure of the asymptotic quasi-periodic measure can then lead to an invariant measure of the lifted semigroup. |
| title | Entrance measures and dynamics for time-inhomogeneous McKean-Vlasov stochastic differential equations |
| topic | Probability 60H10, 60B10, 37A50 |
| url | https://arxiv.org/abs/2604.19187 |