Singular dissipative stochastic equations in Hilbert spaces

2002 ◽  
Vol 124 (2) ◽  
pp. 261-303 ◽  
Author(s):  
Giuseppe Da Prato ◽  
Michael Röckner
Keyword(s):  
Hilbert Spaces ◽  
Stochastic Equations

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

scholarly journals Stochastic model reduction: convergence and applications to climate equations

2021 ◽  
Author(s):  
Sigurd Assing ◽  
Franco Flandoli ◽  
Umberto Pappalettera
Keyword(s):  
Stochastic Model ◽  
Model Reduction ◽  
Hilbert Spaces ◽  
Evolution Equations ◽  
Climate Modeling ◽  
Stochastic Equations ◽  
Weak And Strong Convergence ◽  
Uhlenbeck Process ◽  
Infinite Dimensional ◽  
Reduced Equations

AbstractWe study stochastic model reduction for evolution equations in infinite-dimensional Hilbert spaces and show the convergence to the reduced equations via abstract results of Wong–Zakai type for stochastic equations driven by a scaled Ornstein–Uhlenbeck process. Both weak and strong convergence are investigated, depending on the presence of quadratic interactions between reduced variables and driving noise. Finally, we are able to apply our results to a class of equations used in climate modeling.

scholarly journals Singular dissipative stochastic equations in Hilbert spaces

2008 ◽  
Vol 143 (3-4) ◽  
pp. 659-664 ◽  
Author(s):  
Giuseppe Da Prato ◽  
Michael Röckner
Keyword(s):  
Hilbert Spaces ◽  
Stochastic Equations
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