Stochastic partial differential equations (SPDE) are partial differential equations (PDE) with a `noise term’. One can think of these as a semi-martingale in a function space or a space of distributions with a drift (a bounded variation process involving a second order elliptic partial differential operator ) and a noise term which is a martingale. When the martingale term is suitably structured, the solutions of these SPDE’s are closely related to certain finite dimensional diffusion processes and may be viewed as generalized solutions of the classical stochastic differential equations of Ito, Stroock-Varadhan and others. In this talk [based on Rajeev and Thangavelu (2008) and Rajeev (2010)], we describe how the expected values of the solutions give rise to solutions of PDE’s associated with the diffusion.

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Last updated: 11 Dec 2023