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Large deviation principle for a backward stochastic differential equation driven by $G$-Brownian motion with subdifferential operator

Abdoulaye Soumana Hima, Ibrahim Dakaou

Abstract

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.

Large deviation principle for a backward stochastic differential equation driven by $G$-Brownian motion with subdifferential operator

Abstract

In this paper, we study a large deviation principle for the solution of a backward stochastic differential equation driven by -Brownian motion with subdifferential operator.

Paper Structure

This paper contains 6 sections, 14 theorems, 90 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Large deviations for $G$-SDEs
  4. Large deviations for $G$-BSDEs with subdifferential operator
  5. Assumptions and problem formulation
  6. Convergence and large deviation principle for the solution of the backward equation

Key Result

Theorem 2.8

Hu2009Denis2011. There exists a weakly compact set $\mathcal{P}\subset\mathcal{M}_1(\Omega_T)$, the set of probability measures on $(\Omega_T, \mathcal{B}(\Omega_T))$, such that $\mathcal{P}$ is called a set that represents $\widehat{\mathbb{E}}$.

Theorems & Definitions (28)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Remark 2.5
  • Definition 2.6
  • Definition 2.7
  • Theorem 2.8
  • Definition 2.9
  • Lemma 2.10
  • ...and 18 more