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
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.
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