The DSTN Fellows
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
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.
Expected result / Main goal:
It’s our hope that the exploration of the topics described in this proposal will lead to mathematically significant results and a wider appreciation and understanding of the interaction between the general theory of stochastic partial differential equations and applications in geometry. As far as can be anticipated, active research will be carried out in all the areas discussed above throughout the duration of the grant and at the end of the grant. It is also anticipated that new ideas discovered during this period that appears promising will be pursued.
Contribution / added value to the project:
The mid-term goal is to build an internationally research group working in the field of stochastic differential equations between the two centers.
Prof. Carlos OGOUYANDJOU, ACE SMIA, IMSP, University Abomey-Calavi, Benin
Prof. Mamadou Abdoul DIOP, ACE MITIC, University Gaston Berger, Senegal
Other contributors on the PhD supervision:
Dr. DJIBRIL MOUSSA Freedath, ACE SMIA, IMSP, University Abomey-Calavi, Benin
Dr. AMOUR GBAGUIDI Amoussou, ACE SMIA, IMSP, University Abomey-Calavi, Benin