Backward doubly SDEs with continuous and stochastic linear growth coefficients

2018 ◽  
Vol 26 (3) ◽  
pp. 175-184 ◽  
Author(s):  
Jean Marc Owo
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Linear Growth ◽  
Doubly Stochastic ◽  
Maximal Solutions ◽  
Minimal And Maximal Solutions

Abstract We study backward doubly stochastic differential equations when the coefficients are continuous with stochastic linear growth. Via an approximation and comparison theorem, the existence of minimal and maximal solutions are obtained.

scholarly journals Comparison Theorems for the Multidimensional BDSDEs and Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Bo Zhu ◽  
Baoyan Han
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Existence Of Solutions ◽  
Minimal Solution ◽  
Comparison Theorems ◽  
Doubly Stochastic

A class of backward doubly stochastic differential equations (BDSDEs) are studied. We obtain a comparison theorem of these multidimensional BDSDEs. As its applications, we derive the existence of solutions for this multidimensional BDSDEs with continuous coefficients. We can also prove that this solution is the minimal solution of the BDSDE.

scholarly journals Generalized Mean-Field Fractional BSDEs With Non-Lipschitz Coefficients

2021 ◽  
Vol 10 (3) ◽  
pp. 77
Author(s):  
Qun Shi
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Comparison Theorem ◽  
Lipschitz Condition ◽  
Linear Growth ◽  
Mean Field ◽  
One Dimensional ◽  
Generalized Mean

In this paper we consider one dimensional generalized mean-field backward stochastic differential equations (BSDEs) driven by fractional Brownian motion, i.e., the generators of our mean-field FBSDEs depend not only on the solution but also on the law of the solution. We first give a totally new comparison theorem for such type of BSDEs under Lipschitz condition. Furthermore, we study the existence of the solution of such mean-field FBSDEs when the coefficients are only continuous and with a linear growth.

scholarly journals Anticipated Generalized Backward Doubly Stochastic Differential Equations

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 114
Author(s):  
Tie Wang ◽  
Jiaxin Yu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Uniqueness Theorem ◽  
Comparison Theorem ◽  
Existence And Uniqueness ◽  
Comparison Theorems ◽  
Existence And Uniqueness Theorem ◽  
New Class ◽  
Doubly Stochastic ◽  
Increasing Process

In this paper, we explore a new class of stochastic differential equations called anticipated generalized backward doubly stochastic differential equations (AGBDSDEs), which not only involve two symmetric integrals related to two independent Brownian motions and an integral driven by a continuous increasing process but also include generators depending on the anticipated terms of the solution (Y, Z). Firstly, we prove the existence and uniqueness theorem for AGBDSDEs. Further, two comparison theorems are obtained after finding a new comparison theorem for GBDSDEs.

scholarly journals Backward Doubly Stochastic Differential Equations with Markov Chains and a Comparison Theorem

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1953
Author(s):  
Ning Ma ◽  
Zhen Wu
Keyword(s):  
Differential Equations ◽  
Markov Chains ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Lipschitz Condition ◽  
Existence And Uniqueness ◽  
Comparison Theorems ◽  
Yosida Approximation ◽  
Uniqueness Of Solutions ◽  
Doubly Stochastic

In this paper we study the existence and uniqueness of solutions for one kind of backward doubly stochastic differential equations (BDSDEs) with Markov chains. By generalizing the Itô’s formula, we study such problem under the Lipschitz condition. Moreover, thanks to the Yosida approximation, we solve such problem under monotone condition. Finally, we give the comparison theorems for such equations under the above two conditions respectively.

scholarly journals Monotonic Limit Properties for Solutions of BSDEs with Continuous Coefficients

2009 ◽  
Vol 2009 ◽  
pp. 1-6 ◽  
Author(s):  
ShengJun Fan ◽  
Xing Song ◽  
Ming Ma
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
One Dimensional ◽  
Maximal Solutions ◽  
Minimal And Maximal Solutions

This paper investigates the monotonic limit properties for the minimal and maximal solutions of certain one-dimensional backward stochastic differential equations with continuous coefficients.

Comparison Theorems for the Multi-Dimensional Backward Doubly Stochastic Differential Equations

2012 ◽  
Vol 166-169 ◽  
pp. 3210-3213 ◽  
Author(s):  
Bao Yan Han
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Comparison Theorems ◽  
Doubly Stochastic

A class of backward doubly stochastic differential equations are studied. We obtain a comparison theorem of these multi-dimensional backward doubly stochastic differential equations.

scholarly journals Backward stochastic differential equations with unbounded generators

2019 ◽  
Vol 19 (01) ◽  
pp. 1950008 ◽  
Author(s):  
Bujar Gashi ◽  
Jiajie Li
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Unique Solution ◽  
Comparison Theorem ◽  
Linear Growth ◽  
Sufficient Conditions ◽  
Backward Stochastic Differential Equations ◽  
Type Condition ◽  
Solution Pair ◽  
Picard Iterations

In this paper, we consider two classes of backward stochastic differential equations (BSDEs). First, under a Lipschitz-type condition on the generator of the equation, which can also be unbounded, we give sufficient conditions for the existence of a unique solution pair. The method of proof is that of Picard iterations and the resulting conditions are new. We also prove a comparison theorem. Second, under the linear growth and continuity assumptions on the possibly unbounded generator, we prove the existence of the solution pair. This class of equations is more general than the existing ones.

scholarly journals Existence of solution for Mean-field Reflected Discontinuous Backward Doubly Stochastic Differential Equation

2020 ◽  
Vol 5 (2) ◽  
pp. 205-216
Author(s):  
Mostapha Abdelouahab Saouli
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Mean Field ◽  
Existence Of Solution ◽  
Maximal Solution ◽  
Existence Of A Solution ◽  
Doubly Stochastic

AbstractIn this paper we prove the existence of a solution for mean-field reflected backward doubly stochastic differential equations (MF-RBDSDEs) with one continuous barrier and discontinuous generator (left-continuous). By a comparison theorem establish here for MF-RBDSDEs, we provide a minimal or a maximal solution to MF-RBDSDEs.

A NOTE ON HOMEOMORPHISM FOR BACKWARD DOUBLY SDEs AND APPLICATIONS

2010 ◽  
Vol 10 (04) ◽  
pp. 549-560 ◽  
Author(s):  
A. AMAN ◽  
M. N'ZI ◽  
J. M. OWO
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Stochastic Partial Differential Equations ◽  
Real Parameter ◽  
Partial Differential ◽  
Doubly Stochastic ◽  
Terminal Values

In this note, we study the class of backward doubly stochastic differential equations (BDSDEs). In our framework, the terminal values depend on a real parameter. Under suitable assumptions and by the help of strict comparison theorem, we show homeomorphism property for the solution. This result is used to study homeomorphism property for quasi-linear stochastic partial differential equations.

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