My research lies in the area of the theoretical analysis of stochastic dynamical systems and their numerical approximations and their inference partial observation. Key area of research include
• Stochastic partial differential equations, in particular the Zakai and the Kushner Stratonovitch equation. These stochastic PDEs govern the evolution of the solution of the continuous time stochastic filtering problem.
• Partially observed Markov chains. These dynamical systems are related to the discrete time filtering problem. My results cover necessary and sufficient for the convergence of particle approximation to the solution of the filtering problem, optimal algorithms and, more recently, necessary conditions for the stability of the partially observed Markov chains.
• Data assimilation and Bayesian inference in particular inference for high dimensional system
• Stochastic differential equations, in particular equations perturbed by degenerate noise and their applications to option pricing.
• Forward-backward stochastic differential equations and their applications to nonlinear option pricing and energy markets