COMPARISON THEOREMS FOR MULTI-DIMENSIONAL GENERAL MEAN-FIELD BDSDES

doi:10.1007/s10473-021-0216-z

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (2): 535-551.doi: 10.1007/s10473-021-0216-z

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COMPARISON THEOREMS FOR MULTI-DIMENSIONAL GENERAL MEAN-FIELD BDSDES

Juan LI¹, Chuanzhi XING¹, Ying PENG²

1. School of Mathematics and Statistics, Shandong University, Weihai 264209, China;
2. Shandong University-Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, China

Received:2020-01-19 Revised:2020-10-26 Online:2021-04-25 Published:2021-04-29
Contact: Chuanzhi XING, Ying PENG E-mail:chuanzhixing@mail.sdu.edu.cn;pengy@sdu.edu.cn
About author:Juan LI,E-mail:juanli@sdu.edu.cn
Supported by:
The work has been supported in part by the NSF of P.R.China (11871037; 11222110), Shandong Province (JQ201202), NSFC-RS (11661130148; NA150344), 111 Project (B12023).

Abstract

Abstract: In this paper we study multi-dimensional mean-field backward doubly stochastic differential equations (BDSDEs), that is, BDSDEs whose coefficients depend not only on the solution processes but also on their law. The first part of the paper is devoted to the comparison theorem for multi-dimensional mean-field BDSDEs with Lipschitz conditions. With the help of the comparison result for the Lipschitz case we prove the existence of a solution for multi-dimensional mean-field BDSDEs with an only continuous drift coefficient of linear growth, and we also extend the comparison theorem to such BDSDEs with a continuous coefficient.

Key words: Backward doubly stochastic differential equations, mean-field, multi-dimensional comparison theorem, continuous condition

CLC Number:

60H10

Juan LI, Chuanzhi XING, Ying PENG. COMPARISON THEOREMS FOR MULTI-DIMENSIONAL GENERAL MEAN-FIELD BDSDES[J].Acta mathematica scientia,Series B, 2021, 41(2): 535-551.

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COMPARISON THEOREMS FOR MULTI-DIMENSIONAL GENERAL MEAN-FIELD BDSDES

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