Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-04-30T13:35:06.871Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic behaviour of stochastic quasi dissipative systems

Published online by Cambridge University Press:  15 August 2002

Giuseppe Da Prato
Giuseppe Da Prato*
Affiliation:
Scuola Normale Superiore di Pisa, piazza dei Cavalieri 7, 56126 Pisa, Italy; DaPrato@sms.it.
Get access

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.

Keywords

Stochastic systemsreaction-diffusion equationsinvariant measures.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 587 - 602
Copyright
© EDP Sciences, SMAI, 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

J.M. Bismut, Large deviations and the Malliavin Calculus. Birkhäuser (1984).
H. Brézis, Opérateurs maximaux monotones. North-Holland, Amsterdam (1973).
Cerrai, S., Hille-Yosida, A theorem for weakly continuous semigroups. Semigroup Forum 49 (1994) 349-367. CrossRef
S. Cerrai, Second order PDE's in finite and infinite dimensions. A probabilistic approach. Springer, Lecture Notes in Math. 1762 (2001).
Cerrai, S., Optimal control problems for stochastic reaction-diffusion systems with non Lipschitz coefficients. SIAM J. Control Optim. 39 (2001) 1779-1816. CrossRef
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, Quaderns 11 (1998).
G. Da Prato, A. Debussche and B. Goldys, Invariant measures of non symmetric dissipative stochastic systems. Probab. Theor. Related Fields (to appear).
Da Prato, G., Elworthy, D. and Zabczyk, J., Strong Feller property for stochastic semilinear equations. Stochastic Anal. Appl. 13 (1995) 35-45. CrossRef
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 Notes 229 (1996).
Da Prato, G. and Zabczyk, J., 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 Analysis II (1992) 33-72.
W.H. Fleming and H.M. Soner, Controlled Markov processes and viscosity solutions. Springer-Verlag (1993).
Kato, T., Nonlinear semigroups and evolution equations. J. Math. Soc. Japan 10 (1967) 508-520. CrossRef
K.R. Parthasarathy, Probability measures on metric spaces. Academic Press (1967).