## Research Interests

**Keywords**

###### Stochastic Analysis, Stochastic Partial Differential Equations, Fluid Dynamics, Nonlinear Filtering, Data Assimilation, Mathematical Finance, Particle Approximations, Malliavin Calculus, Machine Learning.

###### 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:

###### • Stochastic partial differential equations, in particular the Nonlinear Fluid Dynamics Equations (Euler, Navier-Stokes, Camassa-Holm, rotating shallow water, quasi-geostrophic, primitive). Also the Zakai and the Kushner Stratonovitch equation which govern the evolution of the solution of the continuous time stochastic filtering problem.

###### • Nonlinear Filtering, including the analysis of the filtering equations, McKean-Vlasov representations, robust filtering, finite dimensional filters, signal dependent measurement noise framework.

###### • Uncertainty quantification, Data assimilation and Bayesian inference in particular inference for high dimensional systems.

###### • 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, necessary conditions for the stability of the partially observed Markov chains.

###### • Stochastic differential equations, equations perturbed by degenerate noise and their applications to option pricing and equations for processes with reflection/absorption at boundary.

###### • Forward-backward stochastic differential equations and their applications to nonlinear option pricing and energy markets

###### I have ongoing projects with the following collaborators: Deniz Akyildiz, Alex Beskos, Bertrand Chapron, Colin Cotter, Martin Clark, Darryl Holm,
Nikolas Kantas, Peter Korn, Tom Kurtz, Ajay Jasra, Joaquin Miguez, Étienne Memin,
Salvador Ortiz-Latorre, Michela Ottobre, Étienne Pardoux, Hamza Ruzayqat, Igor Shevchenko.

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