Martingale problems for conditional distributions of Markov processes.
The Yamada-Watanabe-Engelbert theorem for general stochastic equations and inequalities.
Stationary solutions and forward equations for controlled and singular martingale problems.
Stratonovich stochastic differential equations driven by general semimartingales
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,...
The approximate Euler method for Lévy driven stochastic differential equations
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