PC Seminar: Non-parametric volatility estimation in SPDE driven by white-coloured noise

Abstract: The term "Stochastic partial differential equations" (SPDE) refers to a class of partial differential equations perturbed by a random additional noise. Thus, they can be seen as a generalisation of the notion of stochastic differential equation driven by a Brownian motion.

From a theoretical standpoint, the study of SPDE is a very active topic of research which is currently going through major advances. In practice, SPDE are an important ingredient in the modeling of various physical phenomena.

In this talk, we are going to look at the statistical problem of estimating the volatility of an SPDE with known differential operator. This question has already been adressed in a few recent works, but only in a parametric setting (constant volatility). We are going to build an estimator to tackle the case where the volatility is an unknown function of the solution, as well as looking at a practical implementation of said estimator on simulated datas.

This is a seminar in our seminar series on Probability and Combinatorics (PC).