Approximate McKean–Vlasov representations for a class of SPDEs

Abstract

The solution of a class of linear stochastic partial differential equations is approximated using Clark's robust representation approach. 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.

Keywords:

• stochastic partial differential equations
• particle approximations
• McKean–Vlasov equations
• Zakai equation
• Kushner–Stratonovitch equation
• non-linear diffusions

MSC 2000::

• 60H15
• 60K35
• 35R60
• 93E11

Notes

^1. [email protected]

^2. In (21) the coefficients are those specified in formula (20).

^3. See conditions SM + ES in Section 6.

Additional information

Notes on contributors

Jie Xiong

1. 1. [email protected]