scholarly journals Stochastic PDEs and Infinite Horizon Backward Doubly Stochastic Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Bo Zhu ◽  
Baoyan Han
Keyword(s):  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Continuous Dependence ◽  
Infinite Horizon ◽  
Stochastic Pdes ◽  
Sufficient Condition ◽  
Probabilistic Interpretation ◽  
Doubly Stochastic ◽  
Terminal Values ◽  
Continuous Dependence Theorem

We give a sufficient condition on the coefficients of a class of infinite horizon BDSDEs, under which the infinite horizon BDSDEs have a unique solution for any given square integrable terminal values. We also show continuous dependence theorem and convergence theorem for this kind of equations. A probabilistic interpretation for solutions to a class of stochastic partial differential equations is given.

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.

scholarly journals Convergence Theorems for Operators Sequences on Functionals of Discrete-Time Normal Martingales

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Jinshu Chen
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Discrete Time ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Functional Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Convergence Of Operators

We aim to investigate the convergence of operators sequences acting on functionals of discrete-time normal martingales M. We first apply the 2D-Fock transform for operators from the testing functional space S(M) to the generalized functional space S⁎(M) and obtain a necessary and sufficient condition for such operators sequences to be strongly convergent. We then discuss the integration of these operator-valued functions. Finally, we apply the results obtained here and establish the existence and uniqueness of solution to quantum stochastic differential equations in terms of operators acting on functionals of discrete-time normal martingales M. And also we prove the continuity and continuous dependence on initial values of the solution.

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

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.

On smooth approximation for random attractor of stochastic partial differential equations with multiplicative noise

2018 ◽  
Vol 18 (05) ◽  
pp. 1850040 ◽  
Author(s):  
Hongbo Fu ◽  
Xianming Liu ◽  
Jicheng Liu ◽  
Xiangjun Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Random Attractor ◽  
Invariant Sets ◽  
Stochastic Pdes ◽  
Polygonal Approximation ◽  
Smooth Approximation ◽  
Partial Differential ◽  
Random Partial Differential Equations

Wong–Zakai type approximation for stochastic partial differential equations (abbreviate as PDEs) is well studied. Besides the polygonal approximation, a type of smooth noise approximation is considered. After showing the existence of random attractor for a class of random partial differential equations defined on the entire space [Formula: see text], when random color noises tend to white noise, the solutions and invariant sets between original stochastic PDEs and random PDEs are compared. Some continuity results of random attractor in random dynamical systems are indicated.

Sign in / Sign up

Export Citation Format

Share Document