stochastic

Recent developments for stochastic processes and their applications

Ahmed Kebaier, Associate Professor, Laboratory Analysis, Geometry and Application (LAGA), University Sorbonne Paris Nord (USPN)

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KAUST

In this talk, we present our theoretical results recently developed around various types of applications. These results cover asymptotic and non-asymptotic analysis, functional limit theorems, concentration inequalities, and Malliavin calculus techniques elaborated for several classes of stochastic processes. We showcase through concrete examples the role of these results in taking up various challenges at the cutting-edge of modern applied probability.

Particle Approximations For Partially Observed Fluid Dynamics Models

Professor Dan Crisan, Mathematics, Imperial College London

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KAUST

Fluid dynamics models are ubiquitous in a multitude of applications. One of the most important applications of fluid dynamics models is numerical weather prediction. Modern numerical weather prediction combines sophisticated nonlinear fluid dynamics models with increasingly accurate high-dimensional data. This process is called data assimilation and it is performed every day at all major operational weather centers across the world. Data assimilation (DA) requires massive computing capabilities as realistic atmosphere-ocean models typically have billions of degrees of freedom. I will give a short overview of the ongoing research that aims to drastically decrease the required DA computational effort by reducing the dimension of the models involved and using stochastic perturbations to account for the unresolved scales. The incorporation of observation data is done by using particle approximations suitably adapted to solve high-dimensional problems.

Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation

Nikolas Kantas, Associate Professor, Department of Mathematics, Imperial College London

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KAUST

We consider the problem of parameter estimation for a McKean stochastic differential equation, and the associated system of weakly interacting particles. The problem is motivated by many applications in areas such as neuroscience, social sciences (opinion dynamics, cooperative behaviours), financial mathematics, statistical physics. We will first survey some model properties related to propagation of chaos and ergodicity and then move on to discuss the problem of parameter estimation both in offline and on-line settings. In the on-line case, we propose an online estimator, which evolves according to a continuous-time stochastic gradient descent algorithm on the asymptotic log-likelihood of the interacting particle system. The talk will present our convergence results and then show some numerical results for two examples, a linear mean field model and a stochastic opinion dynamics model. This is joint work with Louis Sharrock, Panos Parpas and Greg Pavliotis. Preprint: https://arxiv.org/abs/2106.13751