scholarly journals Comparison and converse comparison theorems for backward stochastic differential equations with Markov chain noise

2016 ◽  
Vol 21 (0) ◽  
Author(s):  
Zhe Yang ◽  
Dimbinirina Ramarimbahoaka ◽  
Robert J. Elliott
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Comparison Theorems

scholarly journals Multi-valued backward stochastic differential equations with regime switching

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ruijuan Deng ◽  
Yong Ren
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Regime Switching ◽  
Original System ◽  
Backward Stochastic Differential Equations ◽  
Lower Semi ◽  
Finite State ◽  
Uniqueness Of The Solution ◽  
Continuous Convex Function

AbstractThe paper considers a class of multi-valued backward stochastic differential equations with subdifferential of a lower semi-continuous convex function with regime switching, whose generator is a continuous-time Markov chain with a finite state space. Firstly, we get the existence and uniqueness of the solution by the penalization method. Secondly, we prove that the solution of the original system is weakly convergent. Finally, we give an application to the homogenization of a class of multi-valued PDEs with Markov chain.

scholarly journals Solutions and comparison theorems for anticipated backward stochastic differential equations with non-Lipschitz generators

2016 ◽  
Vol 12 (4) ◽  
pp. 6139-6147
Author(s):  
Xuecheng XU ◽  
Min Chen
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Comparison Theorems ◽  
One Dimensional

This paper is devoted to solving multidimensional anticipated backward stochastic differential equations (anticipated BSDEs for short) with a kind of non-Lipschitz generators. We establish the existence and uniqueness result for L2 solutions of this kind of anticipated BSDEs, and establish the corresponding one-dimensional comparison theorems for the type of anticipated BSDEs. Our results improve some known results.

Converse Comparison Theorems for Backward Stochastic Differential Equations

2013 ◽  
Vol 411-414 ◽  
pp. 1400-1403
Author(s):  
Xiao Qin Huang ◽  
Wei Hua Jiang ◽  
Xiao Jie Liu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Backward Stochastic Differential Equations ◽  
Comparison Theorems

In this note, we establish a converse comparison theorem for backward stochastic differential equations (BSDEs).

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