Minimisation of distance measures to efficiently capture the macroscale behaviour of stochastic systems

Presented at Special Session: Infinite Dimensional Stochastic Systems and ApplicationsI will present a method to accelerate the simulation of observables of processes determined by stochastic ODEs, motivated by the recent development of generic multiscale frameworks. The technique exploits the separation between the fast time scale on which we compute trajectories and the slow evolution of observables. The algorithm combines short bursts of paths simulation with extrapolation of a number of moments forward in time. I will concentrate on the crucial step -- how to obtain, after extrapolation, a new ensemble of particles/replicas compatible with given moments. To deal with this inference problem, we introduce the matching operator based on the minimisation of suitable distance between probability distributions. I am going to discuss the generic properties of this operator that allow to establish the theorem on the order of convergence of our method. As a particular example, I will present the matching based on the logarithmic entropy that also provides a convenient numerical approach.status: publishe