HOUNKPE Onésime

Affiliated project: EVSAR

Affiliated ACE: Université d’Abomey-Calavi / SMIA & Université Gaston Berger / MITIC

Title: Continuous-time stochastic processes and geometry

Starting date: 01/01/2021

Problem statement: 
Stochastic Analysis has arguably entered a golden age in recent years, spectacularly expanding further its mathematical depth while breathing and growing strongly through its many applications in other areas. The field’s ability to model and analyze complex random effects make it indispensable in Physics, Biology, Quantitative Finance, Engineering and Data Science.

In this project, we shall investigate a class of delay stochastic differential equations (SDEs), also known as delay SDEs. We shall study the properties of these equations such as existence and uniqueness of the solution, optimal control and portfolio optimization. We also attend to study existence, regularity and stability of solutions for partial functional differential equations which are described by stochastic differential equations. The aim of this part is to study the existence, the regularity and the stability of solutions of some classes of stochastic partial functional differential equations with infinite delay and deviating arguments in terms involving spatial derivatives. 

To achieve the goal of this project, several results in functional analysis and differential equations will be used. We will use the semigroup theory and the spectral analysis of unbounded linear operators in Banach spaces. For the existence of solutions, we will use fixed point theory, for example Banach fixed point theorem or Schauder fixed point theorem. We are proposing to tackle several questions in our project. Answers will have an impact in the direction of the research in this field.