Particle representations for stochastic partial differential equations
Stochastic partial differential equations arise naturally as limits of finite systems of weighted interacting particles. For a variety of purposes, it is useful to keep the particles in the limit obtaining an infinite exchangeable system of stochastic differential equations for the particle locations and weights. The corresponding de Finetti measure then gives the solution of the SPDE. These representations frequently simplify existence, uniqueness and convergence results. Beginning with the classical McKean-Vlasov limit, the basic results on exchangeable systems along with several examples will be discussed.