EXPLORE-SDE: Explosions for non-markovian and related stochastic differential equations

• Universidad Nacional de Colombia (Colombia)

• Universidad de la República (Uruguay)

• Inria Centre at Université Côte d'Azur, Inria (France)

• Universidad de Valparaíso (UV) (Chile)

• Universidad Adolfo Ibañez (Chile)

• Université de Lille (France)

• Université Paris-Saclay (France)

In this proposal, 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.

In France: 

• Etienne Tanré, researcher, EXPLORE-SDE coordinator, Inria Centre at Université Côte d'Azur, Inria

In Chile: 

• Soledad Torres, researcher, EXPLORE-SDE coordinator, Universidad de Valparaíso

• Héctor Araya, researcher, Universidad Adolfo Ibañez

• Tania Roa,  researcher, Universidad Adolfo Ibañez

In Uruguay: 

• Ernesto Mordecki, researcher, EXPLORE-SDE coordinator, Universidad de la República

In Colombia: 

• Johanna Garzón, researcher, EXPLORE-SDE coordinator, Universidad Nacional de Colombia