A probabilistic interpretation of a non-conservative and path-dependent nonlinear reaction-advection-diffusion system
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917008137781248 |
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| author | Morale, Daniela Tarquini, Leonardo Ugolini, Stefania |
| author_facet | Morale, Daniela Tarquini, Leonardo Ugolini, Stefania |
| contents | Given a reaction-advection-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation via a non-Markovian McKean-Vlasov stochastic differential equation coupled with a Feynman-Kac-type equation. We discuss the well-posedness of such a stochastic model, and establish the propagation of chaos property for the associated interacting particle system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19301 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A probabilistic interpretation of a non-conservative and path-dependent nonlinear reaction-advection-diffusion system Morale, Daniela Tarquini, Leonardo Ugolini, Stefania Probability 60H10, 60H30, 60J60, 65C35, 58J35 Given a reaction-advection-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation via a non-Markovian McKean-Vlasov stochastic differential equation coupled with a Feynman-Kac-type equation. We discuss the well-posedness of such a stochastic model, and establish the propagation of chaos property for the associated interacting particle system. |
| title | A probabilistic interpretation of a non-conservative and path-dependent nonlinear reaction-advection-diffusion system |
| topic | Probability 60H10, 60H30, 60J60, 65C35, 58J35 |
| url | https://arxiv.org/abs/2407.19301 |