Mean field stochastic differential equations with a diffusion coefficient with irregular distributional dependence
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916663989895168 |
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| author | Nykänen, Jani |
| author_facet | Nykänen, Jani |
| contents | We study mean field stochastic differential equations with a diffusion coefficient that depends on the distribution function of the unknown process in a discontinuous manner, which is a type of distribution dependent regime switching. To determine the distribution function we show that under certain conditions these equations can be transformed into SDEs with deterministic coefficients using a Lamperti-type transformation. We prove an existence and uniqueness result and consider cases when the uniqueness may fail or a solution exists only for a finite time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21475 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mean field stochastic differential equations with a diffusion coefficient with irregular distributional dependence Nykänen, Jani Probability 60H10, 60H30 We study mean field stochastic differential equations with a diffusion coefficient that depends on the distribution function of the unknown process in a discontinuous manner, which is a type of distribution dependent regime switching. To determine the distribution function we show that under certain conditions these equations can be transformed into SDEs with deterministic coefficients using a Lamperti-type transformation. We prove an existence and uniqueness result and consider cases when the uniqueness may fail or a solution exists only for a finite time. |
| title | Mean field stochastic differential equations with a diffusion coefficient with irregular distributional dependence |
| topic | Probability 60H10, 60H30 |
| url | https://arxiv.org/abs/2503.21475 |