Backward Doubly SDEs with weak Monotonicity and General Growth Generators

We deal with backward doubly stochastic differential equations (BDSDEs) with a weak monotonicity and general growth generators and a square integrable terminal datum. We show the existence and uniqueness of solutions. As application, we establish the existenceand uniqueness of Sobolev solutions to some semilinear stochastic partial differential equations (SPDEs) with a general growth and a weak monotonicity generators. By probabilistic solution, we mean a solution which is representable throughout a BDSDEs.

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Mean-Field Forward-Backward Doubly Stochastic Differential Equations and Related Nonlocal Stochastic Partial Differential Equations

Abstract and Applied Analysis ◽

10.1155/2014/194341 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10

Author(s):

Qingfeng Zhu ◽

Yufeng Shi

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Stochastic Partial Differential Equations ◽

Existence And Uniqueness ◽

Mean Field ◽

Partial Differential ◽

Existence And Uniqueness Results ◽

Doubly Stochastic ◽

Uniqueness Results

Mean-field forward-backward doubly stochastic differential equations (MF-FBDSDEs) are studied, which extend many important equations well studied before. Under some suitable monotonicity assumptions, the existence and uniqueness results for measurable solutions are established by means of a method of continuation. Furthermore, the probabilistic interpretation for the solutions to a class of nonlocal stochastic partial differential equations (SPDEs) combined with algebra equations is given.

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DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025706002287 ◽

2006 ◽

Vol 09 (01) ◽

pp. 155-168 ◽

Cited By ~ 6

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.

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

Symmetry ◽

10.3390/sym12121953 ◽

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.

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Reflected stochastic partial differential equations with jumps

Stochastics and Dynamics ◽

10.1142/s0219493722500022 ◽

2021 ◽

pp. 2250002

Author(s):

Hongchao Qian ◽

Jun Peng

Keyword(s):

Brownian Motion ◽

Partial Differential Equations ◽

Differential Equations ◽

Stochastic Partial Differential Equations ◽

Existence And Uniqueness ◽

Random Measure ◽

Poisson Random Measure ◽

Uniqueness Of Solutions ◽

Partial Differential ◽

Penalization Method

In this paper, we establish the existence and uniqueness of solutions of reflected stochastic partial differential equations (SPDEs) driven both by Brownian motion and by Poisson random measure in a convex domain. Penalization method plays a crucial role.

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A NOTE ON HOMEOMORPHISM FOR BACKWARD DOUBLY SDEs AND APPLICATIONS

Stochastics and Dynamics ◽

10.1142/s021949371000308x ◽

2010 ◽

Vol 10 (04) ◽

pp. 549-560 ◽

Cited By ~ 1

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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Anticipated backward doubly stochastic differential equations driven by teugels martingales with or without reflecting barrier

Daghestan Electronic Mathematical Reports ◽

10.31029/demr.13.1 ◽

2020 ◽

pp. 1-21

Author(s):

Mostapha Saouli ◽

B. Mansouri

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Existence And Uniqueness ◽

Time Interval ◽

Present Value ◽

Uniqueness Of Solutions ◽

Doubly Stochastic ◽

Teugels Martingales ◽

The Fixed Point Theorem

We are interested in this paper on reflected anticipated backward doubly stochastic differential equations (RABDSDEs) driven by teugels martingales associated with Levy process. We obtain the existence and uniqueness of solutions to these equations by means of the fixed-point theorem where the coefficients of these BDSDEs depend on the future and present value of the solution $\left( Y,Z\right)$. We also show the comparison theorem for a special class of RABDSDEs under some slight stronger conditions. The novelty of our result lies in the fact that we allow the time interval to be infinite.

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