In this project, we are interested in studying explosion criteria and numerical schemes for non-Markovian stochastic differential equations (SDE). Specifically, we propose to work on three main topics. The first one consists of studying explosion criteria for stochastic differential equations with Markovian switching and additive noise derived from a non-Markovian process such as fractional Brownian motion. We plan to develop a numerical scheme to approximate the explosion time. The second part of the proposal consists of studying a class of stochastic functional differential equations. We plan to study explosion criteria as well as a numerical scheme to approximate the explosion time. The third part deals with the study of the characterization of the random time of explosion from a statistical perspective and the estimation of parameters in a nonlinear AR model with fractional Brownian motion noise, which can be considered as a statistical model derived from a stochastic functional differential equation.

This project is organized by Maria Soledad Torres (Universidad de Valparaíso, Chile), Ernesto Mordecki (Universidad de la República, Uruguay), Johanna Garzón (Universidad Nacional de Colombia, Colombia) and Etienne Tanré (Université Côte d’Azur, Francia) with the participation of Universidad Adolfo Ibañez, Universidad de Chile (Chile), Univ. De Lille, Centre Inria de l’Université de Lorraine and Université Paris Saclay (Francia)