Measure valued solutions for stochastic evolution equations on Hilbert space and their feedback control

2005 ◽  
Vol 25 (1) ◽  
pp. 129 ◽  
Author(s):  
N.U. Ahmed
Keyword(s):  
Hilbert Space ◽  
Feedback Control ◽  
Evolution Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

scholarly journals Controllability of semilinear stochastic evolution equations in Hilbert space

2001 ◽  
Vol 14 (4) ◽  
pp. 329-339 ◽  
Author(s):  
P. Balasubramaniam ◽  
J. P. Dauer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Evolution Equations ◽  
Stochastic Partial Differential Equation ◽  
Semigroup Theory ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

Controllability of semilinear stochastic evolution equations is studied by using stochastic versions of the well-known fixed point theorem and semigroup theory. An application to a stochastic partial differential equation is given.

scholarly journals Second-order neutral stochastic evolution equations with heredity

2004 ◽  
Vol 2004 (2) ◽  
pp. 177-192 ◽  
Author(s):  
Mark A. McKibben
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Continuous Dependence ◽  
Evolution Equations ◽  
Separable Hilbert Space ◽  
Second Order ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Integro Differential Equation ◽  
Real Separable Hilbert Space

Existence, continuous dependence, and approximation results are established for a class of abstract second-order neutral stochastic evolution equations with heredity in a real separable Hilbert space. A related integro-differential equation is also mentioned, as well as an example illustrating the theory.

scholarly journals On a Class of Measure-Dependent Stochastic Evolution Equations Driven by fBm

2007 ◽  
Vol 2007 ◽  
pp. 1-26 ◽  
Author(s):  
Eduardo Hernandez ◽  
David N. Keck ◽  
Mark A. McKibben
Keyword(s):  
Hilbert Space ◽  
Brownian Motion ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Evolution Equations ◽  
Separable Hilbert Space ◽  
Probability Measures ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Real Separable Hilbert Space

We investigate a class of abstract stochastic evolution equations driven by a fractional Brownian motion (fBm) dependent upon a family of probability measures in a real separable Hilbert space. We establish the existence and uniqueness of a mild solution, a continuous dependence estimate, and various convergence and approximation results. Finally, the analysis of three examples is provided to illustrate the applicability of the general theory.

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