Approximate McKean-Vlasov Representations for a class of SPDEs
| dc.creator | Crisan, Dan | |
| dc.creator | Xiong, Jie | |
| dc.date | 2005-10-31 | |
| dc.date.accessioned | 2026-07-07T06:48:08Z | |
| dc.date.available | 2026-07-07T06:48:08Z | |
| dc.description | The solution $\vartheta =(\vartheta_{t})_{t\geq 0}$ of a class of linear stochastic partial differential equations is approximated using Clark's robust representation approach (\cite{c}, \cite{cc}). The ensuing approximations are shown to coincide with the time marginals of solutions of a certain McKean-Vlasov type equation. We prove existence and uniqueness of the solution of the McKean-Vlasov equation. The result leads to a representation of $\vartheta $as a limit of empirical distributions of systems of equally weighted particles. In particular, the solution of the Zakai equation and that of the Kushner-Stratonovitch equation (the two main equations of nonlinear filtering) are shown to be approximated the empirical distribution of systems of particles that have equal weights (unlike those presented in \cite{kj1} and \cite{kj2}) and do not require additional correction procedures (such as those introduced in \cite{dan3}, \cite{dan4}, \cite{dmm}, etc). | |
| dc.identifier | https://arxiv.org/abs/math/0510668 | |
| dc.identifier | http://arxiv.org/abs/math/0510668 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103885 | |
| dc.subject | Probability | |
| dc.subject | 60H15, 60K35, 35R60, 93E11 | |
| dc.title | Approximate McKean-Vlasov Representations for a class of SPDEs | |
| dc.type | text |