Stochastic Analysis, Nonlinear Filtering, Data Assimilation, Monte Carlo Methods, Particle Approximations, Malliavin Calculus,
Stochastic Partial Differential Equations, Mathematical Finance, .
My research lies in the area of the theoretical analysis of stochastic dynamical systems, their numerical approximations and their inference partial observation. Key area of research include
• Linear and nonlinear stochastic partial differential equations (Camassa-Holm, Euler, Zakai )
• 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.
• Uncertainty quantification, 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
I have ongoing projects with the following collaborators: Julien Barré, Tom Cass, Jean-Francois Chassagneux, Colin Cotter, Martin Clark,
Pierre Del Moral, Thierry Goudon, Nikolas Kantas, Tom Kurtz, Joaquin Miguez,
Marvin Mueller, Salvador Ortiz-Latorre, Étienne Pardoux, Nizar Touzi, Jie Xiong.