scholarly journals Existence and Stability for Stochastic Partial Differential Equations with Infinite Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan ◽  
Xichao Sun
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Partial Differential ◽  
Sample Paths ◽  
Existence And Stability ◽  
Stability In Mean Square

We consider a class of neutral stochastic partial differential equations with infinite delay in real separable Hilbert spaces. We derive the existence and uniqueness of mild solutions under some local Carathéodory-type conditions and also exponential stability in mean square of mild solutions as well as its sample paths. Some known results are generalized and improved.

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.

Towards sample path estimates for fast–slow stochastic partial differential equations

2018 ◽  
Vol 30 (5) ◽  
pp. 1004-1024 ◽  
Author(s):  
MANUEL V. GNANN ◽  
CHRISTIAN KUEHN ◽  
ANNE PEIN
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Sample Path ◽  
Slow Manifold ◽  
Mathematical Tool ◽  
Partial Differential ◽  
Sample Paths ◽  
Time Period ◽  
Short Time

Estimates for sample paths of fast–slow stochastic ordinary differential equations have become a key mathematical tool relevant for theory and applications. In particular, there have been breakthroughs by Berglund and Gentz to prove sharp exponential error estimates. In this paper, we take the first steps in order to generalise this theory to fast–slow stochastic partial differential equations. In a simplified setting with a natural decomposition into low- and high-frequency modes, we demonstrate that for a short-time period the probability for the corresponding sample path to leave a neighbourhood around the stable slow manifold of the system is exponentially small as well.

scholarly journals On the Convergence of Solutions for SPDEs under Perturbation of the Domain

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Zhongkai Guo ◽  
Jicheng Liu ◽  
Wenya Wang
Keyword(s):  
Boundary Condition ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Dirichlet Boundary Condition ◽  
Stochastic Partial Differential Equations ◽  
Dirichlet Boundary ◽  
Mild Solutions ◽  
Partial Differential ◽  
Domain Perturbation ◽  
Convergence Of Solutions

We investigate the effect of domain perturbation on the behavior of mild solutions for a class of semilinear stochastic partial differential equations subject to the Dirichlet boundary condition. Under some assumptions, we obtain an estimate for the mild solutions under changes of the domain.

Sign in / Sign up

Export Citation Format

Share Document