The multiplicative ergodic theorem for McKean-Vlasov SDEs
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916096093716480 |
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| author | Cheng, Xianjin Liu, Zhenxin Zhang, Lixin |
| author_facet | Cheng, Xianjin Liu, Zhenxin Zhang, Lixin |
| contents | In this paper, we establish the multiplicative ergodic theorem for McKean-Vlasov stochastic differential equations, in which the Lyapunov exponent is defined using the upper limit. The reasonability of this definition is illustrated through an example; i.e., even when the coefficients are regular enough and their first-order derivatives are bounded, the upper limit cannot be replaced by a limit, as the limit may not exist. Furthermore, the example reveals how the dependence on distribution significantly influences the dynamics of the system and evidently distinguishes McKean-Vlasov stochastic differential equations from classical stochastic differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09702 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The multiplicative ergodic theorem for McKean-Vlasov SDEs Cheng, Xianjin Liu, Zhenxin Zhang, Lixin Dynamical Systems Probability 34D08, 37A50, 37H15, 60H10 In this paper, we establish the multiplicative ergodic theorem for McKean-Vlasov stochastic differential equations, in which the Lyapunov exponent is defined using the upper limit. The reasonability of this definition is illustrated through an example; i.e., even when the coefficients are regular enough and their first-order derivatives are bounded, the upper limit cannot be replaced by a limit, as the limit may not exist. Furthermore, the example reveals how the dependence on distribution significantly influences the dynamics of the system and evidently distinguishes McKean-Vlasov stochastic differential equations from classical stochastic differential equations. |
| title | The multiplicative ergodic theorem for McKean-Vlasov SDEs |
| topic | Dynamical Systems Probability 34D08, 37A50, 37H15, 60H10 |
| url | https://arxiv.org/abs/2401.09702 |