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Conditional distributions, exchangeable particle systems, and stochastic partial differential equations

Dan Crisan; Thomas G. Kurtz; Yoonjung Lee — 2014

Annales de l'I.H.P. Probabilités et statistiques

Stochastic partial differential equations (SPDEs) whose solutions are probability-measure-valued processes are considered. Measure-valued processes of this type arise naturally as de Finetti measures of infinite exchangeable systems of particles and as the solutions for filtering problems. In particular, we consider a model of asset price determination by an infinite collection of competing traders. Each trader’s valuations of the assets are given by the solution of a stochastic differential equation,...

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