𝕃<sup>2</sup>-solutions of multidimensional generalized BSDEs with weak monotonicity and general growth generators in a general filtration-Reference-Cited by-同舟云学术

𝕃²-solutions of multidimensional generalized BSDEs with weak monotonicity and general growth generators in a general filtration

Published:2023-02-28 Issue:2 Volume:31 Page:117-139
ISSN:0926-6364
Container-title:Random Operators and Stochastic Equations
language:en
Short-container-title:

Author:

Belfadli Rachid¹,El Mellali Tarik²,Fakhouri Imade³^ORCID,Ouknine Youssef⁴

Affiliation:

1. Department of Mathematics , Research Group of Geometry, Stochastic Analysis and Applications, Faculty of Sciences and Techniques , Cadi Ayyad University , B.P. 549 , Marrakesh , 40000 , Morocco

2. Department of Mathematics , Faculty of Sciences Semlalia , Cadi Ayyad University , B.P. 2390 , Marrakesh , 40000 , Morocco

3. Equipe Aide à la Décision, Labo. LISAD, Département de Génie Industriel , Ecole Nationale des Sciences Appliquées , Université Ibn Zohr , B.P. 1136 , Agadir , Morocco

4. Department of Mathematics , Faculty of Sciences Semlalia , Cadi Ayyad University , B.P. 2390 , Marrakesh , 40000; and Mohammed VI Polytechnic University, Africa Business School, Avenue Mohammed Ben Abdellah Regragui, Madinat Al Irfane, BP 6380, RABAT , Morocco

Abstract

Abstract In this paper, we study multidimensional generalized backward stochastic differential equations (GBSDEs), in a general filtration supporting a Brownian motion and an independent Poisson random measure, whose generators are weakly monotone and satisfy a general growth condition with respect to the state variable y. We show that such GBSDEs admit a unique 𝕃 2

{\mathbb{L}^{2}}

-solution. The main tools and techniques used in the proofs are the a-priori-estimation, the convolution approach, the iteration, the truncation, and the Bihari inequality.

Publisher

Walter de Gruyter GmbH

Subject

Statistics and Probability,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/rose-2023-2002/pdf

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