Reflected backward stochastic differential equations with time-delayed generators

2018 ◽  
Vol 26 (1) ◽  
pp. 11-22
Author(s):  
Navegué Tuo ◽  
Harouna Coulibaly ◽  
Auguste Aman
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Penalization Method ◽  
One Dimensional

AbstractThis paper is devoted to establish an existence and uniqueness result of one-dimensional reflected backward stochastic differential equations with time-delayed generators (RBSDEs with time-delayed generators, in short). Our proof is based on approximation via a penalization method.

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.

DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

scholarly journals Backward stochastic differential equations with stochastic monotone coefficients

2004 ◽  
Vol 2004 (4) ◽  
pp. 317-335 ◽  
Author(s):  
K. Bahlali ◽  
A. Elouaflin ◽  
M. N'zi
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Nonlinear Pdes ◽  
Monotonicity Condition ◽  
Stochastic Monotonicity ◽  
Monotone Coefficients ◽  
Terminal Time

We prove an existence and uniqueness result for backward stochastic differential equations whose coefficients satisfy a stochastic monotonicity condition. In this setting, we deal with both constant and random terminal times. In the random case, the terminal time is allowed to take infinite values. But in a Markovian framework, that is coupled with a forward SDE, our result provides a probabilistic interpretation of solutions to nonlinear PDEs.

Predictable solution for reflected BSDEs when the obstacle is not right-continuous

2020 ◽  
Vol 28 (4) ◽  
pp. 269-279
Author(s):  
Mohamed Marzougue ◽  
Mohamed El Otmani
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Random Measure ◽  
Backward Stochastic Differential Equations ◽  
Poisson Random Measure ◽  
One Dimensional ◽  
General Filtration ◽  
Reflected Bsdes

AbstractIn the present paper, we consider reflected backward stochastic differential equations when the reflecting obstacle is not necessarily right-continuous in a general filtration that supports a one-dimensional Brownian motion and an independent Poisson random measure. We prove the existence and uniqueness of a predictable solution for such equations under the stochastic Lipschitz coefficient by using the predictable Mertens decomposition.

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.

Comparison Theorem for any Solutions of Backward Stochastic Differential Equations and its Application

2012 ◽  
Vol 524-527 ◽  
pp. 3801-3804
Author(s):  
Shi Yu Li ◽  
Wu Jun Gao ◽  
Jin Hui Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Equations ◽  
Local Martingale ◽  
One Dimensional ◽  
Lipschitz Continuous ◽  
The One ◽  
Uniformly Lipschitz

ƒIn this paper, we study the one-dimensional backward stochastic equations driven by continuous local martingale. We establish a generalized the comparison theorem for any solutions where the coefficient is uniformly Lipschitz continuous in z and is equi-continuous in y.

scholarly journals Solutions to BSDEs Driven by Multidimensional Fractional Brownian Motions

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Jie Miao ◽  
Xu Yang
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Conditional Expectation ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
Fixed Point Principle ◽  
Fractional Ito Formula

We study more general backward stochastic differential equations driven by multidimensional fractional Brownian motions. Introducing the concept of the multidimensional fractional (or quasi-) conditional expectation, we study some of its properties. Using the quasi-conditional expectation and multidimensional fractional Itô formula, we obtain the existence and uniqueness of the solutions to BSDEs driven by multidimensional fractional Brownian motions, where a fixed point principle is employed. Finally, solutions to linear fractional backward stochastic differential equations are investigated.

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