Stochastic Partial Differential Equations in Hilbert Spaces

2014 ◽  
pp. 105-134
Author(s):  
Vidyadhar Mandrekar ◽  
Barbara Rüdiger
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Partial Differential

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 Optimal control for stochastic partial differential equations and viscosity solutions of Bellman equations

1991 ◽  
Vol 123 ◽  
pp. 13-37 ◽  
Author(s):  
Makiko Nisio
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Equations ◽  
Viscosity Solutions ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Infinite Dimensions ◽  
Partial Differential ◽  
Bellman Equations

Recently M. G. Crandall and P. L. Lions developed the viscosity theory on nonlinear equations in infinite dimensions and optimal control in Hilbert spaces, in two series of papers, [1], [4].

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.

scholarly journals Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

2021 ◽  
Author(s):  
Shohei Nakajima
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Stochastic Partial Differential Equations ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Continuity Theorem ◽  
Existence Of Weak Solutions ◽  
One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

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