Nonlinear filtering with signal dependent observation noise.
Probabilistic methods for semilinear partial differential equations. Applications to finance
With the pioneering work of [Pardoux and Peng, (1990) 55–61; Pardoux and Peng, (1992) 200–217]. We have at our disposal stochastic processes which solve the so-called . These processes provide us with a Feynman-Kac representation for the solutions of a class of nonlinear partial differential equations (PDEs) which appear in many applications in the field of Mathematical Finance. Therefore there is a great interest among both practitioners and theoreticians to...
Conditional distributions, exchangeable particle systems, and stochastic partial differential equations
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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