# Lp SOLUTIONS FOR GENERAL TIME INTERVAL MULTIDIMENSIONAL BSDES WITH WEAK MONOTONICITY AND GENERAL GROWTH GENERATORS

• Dong, Yongpeng (School of Mathematics China University of Mining and Technology) ;
• Fan, Shengjun (School of Mathematics China University of Mining and Technology)
• Accepted : 2017.11.07
• Published : 2018.07.31
• 167 8

#### 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

#### Acknowledgement

Supported by : Central Universities

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