Asymptotic behaviour of stochastic quasi dissipative systems
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 8, page 587-602
- ISSN: 1292-8119
Access Full Article
topAbstract
topHow to cite
topPrato, Giuseppe Da. "Asymptotic behaviour of stochastic quasi dissipative systems." ESAIM: Control, Optimisation and Calculus of Variations 8 (2010): 587-602. <http://eudml.org/doc/90661>.
@article{Prato2010,
abstract = {
We prove uniqueness of the invariant measure and the exponential convergence to equilibrium
for a stochastic dissipative system whose drift is perturbed by a bounded function.
},
author = {Prato, Giuseppe Da},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Stochastic systems; reaction-diffusion equations; invariant measures.; stochastic systems; invariant measures},
language = {eng},
month = {3},
pages = {587-602},
publisher = {EDP Sciences},
title = {Asymptotic behaviour of stochastic quasi dissipative systems},
url = {http://eudml.org/doc/90661},
volume = {8},
year = {2010},
}
TY - JOUR
AU - Prato, Giuseppe Da
TI - Asymptotic behaviour of stochastic quasi dissipative systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 8
SP - 587
EP - 602
AB -
We prove uniqueness of the invariant measure and the exponential convergence to equilibrium
for a stochastic dissipative system whose drift is perturbed by a bounded function.
LA - eng
KW - Stochastic systems; reaction-diffusion equations; invariant measures.; stochastic systems; invariant measures
UR - http://eudml.org/doc/90661
ER -
References
top- J.M. Bismut, Large deviations and the Malliavin Calculus. Birkhäuser (1984).
- H. Brézis, Opérateurs maximaux monotones. North-Holland, Amsterdam (1973).
- S. Cerrai, A Hille-Yosida theorem for weakly continuous semigroups. Semigroup Forum49 (1994) 349-367.
- S. Cerrai, Second order PDE's in finite and infinite dimensions. A probabilistic approach. Springer, Lecture Notes in Math. 1762 (2001).
- S. Cerrai, Optimal control problems for stochastic reaction-diffusion systems with non Lipschitz coefficients. SIAM J. Control Optim.39 (2001) 1779-1816.
- S. Cerrai, Stationary Hamilton-Jacobi equations in Hilbert spaces and applications to a stochastic optimal control problem. SIAM J. Control Optim. (to appear).
- G. Da Prato, Stochastic evolution equations by semigroups methods. Centre de Recerca Matematica, Barcelona, Quaderns11 (1998).
- G. Da Prato, A. Debussche and B. Goldys, Invariant measures of non symmetric dissipative stochastic systems. Probab. Theor. Related Fields (to appear).
- G. Da Prato, D. Elworthy and J. Zabczyk, Strong Feller property for stochastic semilinear equations. Stochastic Anal. Appl.13 (1995) 35-45.
- G. Da Prato and M. Röckner, Singular dissipative stochastic equations in Hilbert spaces, Preprint. S.N.S. Pisa (2001).
- G. Da Prato and J. Zabczyk, Stochastic equations in infinite dimensions. Cambridge University Press (1992).
- G. Da Prato and J. Zabczyk, Ergodicity for Infinite Dimensional Systems. Cambridge University Press, London Math. Soc. Lecture Notes229 (1996).
- G. Da Prato and J. Zabczyk, Differentiability of the Feynman-Kac semigroup and a control application. Rend. Mat. Accad. Lincei.8 (1997) 183-188.
- E.B. Dynkin, Markov Processes, Vol. I. Springer-Verlag (1965).
- K.D. Elworthy, Stochastic flows on Riemannian manifolds, edited by M.A. Pinsky and V. Wihstutz. Birkhäuser, Diffusion Processes and Related Problems in AnalysisII (1992) 33-72.
- W.H. Fleming and H.M. Soner, Controlled Markov processes and viscosity solutions. Springer-Verlag (1993).
- T. Kato, Nonlinear semigroups and evolution equations. J. Math. Soc. Japan10 (1967) 508-520.
- K.R. Parthasarathy, Probability measures on metric spaces. Academic Press (1967).
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.