arXiv subjects
Publications and source records attributed to Abdoulaye Soumana Hima.
In this paper, we study a large deviation principle for the solution of a backward stochastic differential equation driven by $G$-Brownian motion with subdifferential operator.
In this paper, we consider forward-backward stochastic differential equation driven by $G$-Brownian motion ($G$-FBSDEs in short) with small parameter $\varepsilon > 0$. We study the asymptotic behavior of the solution of the backward equation and establish a large deviation principle for the corresponding process.
In this paper, we first review the penalization method for solving deterministic Skorokhod problems in non-convex domains and establish estimates for problems with $α$-Hölder continuous functions. With the help of these results obtained previously for deterministic problems, we pathwisely define the reflected $G$-Brownian motion and prove its existence and uniqueness in a Banach space. Finally, multi-dimensional reflected stochastic differential equations driven by $G$-Brownian motion are investigated via a fixed-point argument.
In this paper, we consider backward stochastic differential equations driven by $G$-Brownian motion (GBSDEs) under quadratic assumptions on coefficients. We prove the existence and uniqueness of solution for such equations. On the one hand, a priori estimates are obtained by applying the Girsanov type theorem in the $G$-framework, from which we deduce the uniqueness. On the other hand, to prove the existence of solutions, we first construct solutions for discrete GBSDEs by solving corresponding fully nonlinear PDEs, and then approximate solutions for general quadratic GBSDEs in Banach spaces.