Access the full text.
Sign up today, get DeepDyve free for 14 days.
J. Zabczyk (1999)
Parabolic equations on Hilbert spaces
G. Prato, S. Kwapieň, J. Zabczyk (1988)
Regularity of solutions of linear stochastic equations in hilbert spacesStochastics An International Journal of Probability and Stochastic Processes, 23
M. Freĭdlin, A. Ventt︠s︡elʹ (1984)
Random Perturbations of Dynamical Systems
G. Prato, J. Zabczyk (2008)
Stochastic Equations in Infinite Dimensions
Y. Kabanov, S. Pergamenshchikov (2002)
Two-scale stochastic systems
H. Kushner (1990)
Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems
M. Fuhrman, G. Tessitore (2002)
Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal controlAnnals of Probability, 30
S. Peszat, J. Zabczyk (1995)
Strong Feller Property and Irreducibility for Diffusions on Hilbert SpacesAnnals of Probability, 23
G. Prato, J. Zabczyk (1996)
Ergodicity for Infinite Dimensional Systems: Invariant measures for stochastic evolution equations
The present paper studies the problem of singular perturbation in the infinite-dimensional framework and gives a Hilbert-space-valued stochastic version of the Tikhonov theorem. We consider a nonlinear system of Hilbert-space-valued equations for a "slow" and a "fast" variable; the system is strongly coupled and driven by linear unbounded operators generating a C 0 -semigroup and independent cylindrical Brownian motions. Under well-established assumptions to guarantee the existence and uniqueness of mild solutions, we deduce the required stability of the system from a dissipativity condition on the drift of the fast variable. We avoid differentiability assumptions on the coefficients which would be unnatural in the infinite-dimensional framework.
Applied Mathematics and Optimization – Springer Journals
Published: Mar 1, 2006
Access the full text.
Sign up today, get DeepDyve free for 14 days.