Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2018; 33(3): 985-999

Online first article July 9, 2018      Printed July 31, 2018

https://doi.org/10.4134/CKMS.c170305

Copyright © The Korean Mathematical Society.

$L^p$ solutions for general time interval multidimensional BSDEs with weak monotonicity and general growth generators

Yongpeng Dong, Shengjun Fan

China University of Mining and Technology, China University of Mining and Technology

Abstract

This paper is devoted to the existence and uniqueness of $L^p\,(p>1)$ solutions for general time interval multidimensional backward stochastic differential equations (BSDEs for short), where the generator $g$ satisfies a $(p\wedge 2)$-order weak monotonicity condition in $y$ and a Lipschitz continuity condition in $z$, both non-uniformly in $t$. The corresponding stability theorem and comparison theorem are also proved.

Keywords: backward stochastic differential equation, general time interval, existence and uniqueness, weak monotonicity, comparison theorem, stability theorem

MSC numbers: 60H10