scholarly journals REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A LÉVY PROCESS

2009 ◽  
Vol 50 (4) ◽  
pp. 486-500 ◽  
Author(s):  
YONG REN ◽  
XILIANG FAN
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lévy Process ◽  
Backward Stochastic Differential Equations ◽  
Levy Process ◽  
Penalization Method ◽  
Lower Semi ◽  
Uniqueness Of The Solution ◽  
Teugels Martingales ◽  
Continuous Convex Function

AbstractIn this paper, we deal with a class of reflected backward stochastic differential equations (RBSDEs) corresponding to the subdifferential operator of a lower semi-continuous convex function, driven by Teugels martingales associated with a Lévy process. We show the existence and uniqueness of the solution for RBSDEs by means of the penalization method. As an application, we give a probabilistic interpretation for the solutions of a class of partial differential-integral inclusions.

Reflected generalized BSDEs with discontinuous barriers driven by a Lévy process

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohamed El Otmani
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lévy Process ◽  
Backward Stochastic Differential Equations ◽  
Levy Process ◽  
Uniqueness Of The Solution ◽  
Teugels Martingales

Abstract This article deals with the reflected and doubly reflected generalized backward stochastic differential equations when the noise is given by Brownian motion and Teugels martingales associated with an independent pure jump Lévy process. We prove the existence and the uniqueness of the solution for these equations with monotone generators and right continuous left limited obstacles.

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.

Some Properties of BSDEs Driven by a Simple Lévy Process with Continuous Coeffcient

2011 ◽  
Vol 50-51 ◽  
pp. 288-292
Author(s):  
Shi Qiu Zheng ◽  
Dian Chuan Jin ◽  
Shuai Zhang ◽  
Yan Mei Yang ◽  
Jin Peng Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Lévy Process ◽  
Linear Growth ◽  
Backward Stochastic Differential Equations ◽  
Levy Process

In this paper, we mainly study the properties of solutions of backward stochastic differential equations (BSDEs) driven by a simple Lévy process, whose coefficient coeffcient is continuous with linear growth. A comparison theorem for solutions of the equations are obtained, we also show the equation has either one or uncountably many solutions.

WEAK SOLUTIONS OF SEMILINEAR PDEs WITH OBSTACLE(S) IN SOBOLEV SPACES AND THEIR PROBABILISTIC INTERPRETATION VIA THE RFBSDEs AND DRFBSDEs

2008 ◽  
Vol 08 (02) ◽  
pp. 247-269 ◽  
Author(s):  
YOUSSEF OUKNINE ◽  
DJIBRIL NDIAYE
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Probabilistic Interpretation ◽  
Penalization Method ◽  
Semilinear Pdes ◽  
Uniqueness Of The Solution

We prove the existence and uniqueness of the solution of a semilinear PDEs with obstacle(s) under Lipschitz condition. We give a probabilistic interpretation of the solution in Sobolev spaces using reflected forward–backward stochastic differential equations, doubly reflected forward–backward stochastic differential equations and the penalization method.

scholarly journals Backward Stochastic Differential Equations Driven by G-Brownian Motion with Double Reflections

2020 ◽  
Author(s):  
Hanwu Li ◽  
Yongsheng Song
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Backward Stochastic Differential Equations ◽  
Penalization Method ◽  
Priori Estimates ◽  
Uniqueness And Existence

Abstract In this paper, we study the reflected backward stochastic differential equations driven by G-Brownian motion with two reflecting obstacles, which means that the solution lies between two prescribed processes. A new kind of approximate Skorohod condition is proposed to derive the uniqueness and existence of the solutions. The uniqueness can be proved by a priori estimates and the existence is obtained via a penalization method.

scholarly journals Lp Solutions of BSDEs with Stochastic Lipschitz Condition

2007 ◽  
Vol 2007 ◽  
pp. 1-14 ◽  
Author(s):  
Jiajie Wang ◽  
Qikang Ran ◽  
Qihong Chen
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lipschitz Condition ◽  
Existence And Uniqueness ◽  
Special Class ◽  
Lipschitz Continuity ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Of The Solution ◽  
Lp Solutions

We are concerned with the solutions of a special class of backward stochastic differential equations which are driven by a Brownian motion, where the uniform Lipschitz continuity is replaced by a stochastic one. We prove the existence and uniqueness of the solution in Lp with p>1.

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