scholarly journals Singular stochastic equations on Hilbert spaces: Harnack inequalities for their transition semigroups

2009 ◽  
Vol 257 (4) ◽  
pp. 992-1017 ◽  
Author(s):  
Giuseppe Da Prato ◽  
Michael Röckner ◽  
Feng-Yu Wang
Keyword(s):  
Hilbert Spaces ◽  
Stochastic Equations ◽  
Harnack Inequalities ◽  
Transition Semigroups

On the norm continuity of transition semigroups in Hilbert spaces

1998 ◽  
Vol 70 (1) ◽  
pp. 52-56 ◽  
Author(s):  
Wolfgang Desch ◽  
Abdelaziz Rhandi
Keyword(s):  
Hilbert Spaces ◽  
Norm Continuity ◽  
Transition Semigroups

scholarly journals Almost Automorphic Solutions to Nonautonomous Stochastic Functional Integrodifferential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Li Xi-liang ◽  
Han Yu-liang
Keyword(s):  
Hilbert Spaces ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Stochastic Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Banach Contraction ◽  
Stability Results ◽  
Stochastic Functional

This paper concerns the square-mean almost automorphic solutions to a class of abstract semilinear nonautonomous functional integrodifferential stochastic evolution equations in real separable Hilbert spaces. Using the so-called “Acquistapace-Terreni” conditions and Banach contraction principle, the existence, uniqueness, and asymptotical stability results of square-mean almost automorphic mild solutions to such stochastic equations are established. As an application, square-mean almost automorphic solution to a concrete nonautonomous integro-differential stochastic evolution equation is analyzed to illustrate our abstract results.

Approximate controllability of stochastic equations in a Hilbert space with fractional Brownian motions

2014 ◽  
Vol 15 (01) ◽  
pp. 1550005 ◽  
Author(s):  
Mo Chen
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Additive Noise ◽  
Sufficient Conditions ◽  
Stochastic Equations ◽  
Hurst Parameter ◽  
Banach Fixed Point Theorem ◽  
Fractional Brownian Motions

In this paper, the approximate controllability for semilinear stochastic equations in Hilbert spaces is studied. The additive noise is the formal derivative of a fractional Brownian motion in a Hilbert space with the Hurst parameter in the interval (½, 1). Sufficient conditions are established. The results are obtained by using the Banach fixed point theorem.

Regularity of solutions of linear stochastic equations in hilbert spaces

Stochastics ◽  
1988 ◽  
Vol 23 (1) ◽  
pp. 1-23 ◽  
Author(s):  
G. Da prato ◽  
S. Kwapieň ◽  
J. Zabczyk
Keyword(s):  
Hilbert Spaces ◽  
Stochastic Equations ◽  
Regularity Of Solutions
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