On sequentially weakly Feller solutions to SPDE’s
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 10 (1999) no. 2, pp. 69-78.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

A rather general class of stochastic evolution equations in Hilbert spaces whose transition semigroups are Feller with respect to the weak topology is found, and consequences for existence of invariant measures are discussed.
Viene presentata un’ampia classe di equazioni di evoluzione stocastiche in spazi di Hilbert i cui semigruppi di transizione hanno la proprietà di Feller rispetto alla topologia debole; vengono inoltre discusse alcune conseguenze per l’esistenza di misure invarianti.
@article{RLIN_1999_9_10_2_a1,
     author = {Maslowski, Bohdan and Seidler, Jan},
     title = {On sequentially weakly {Feller} solutions to {SPDE{\textquoteright}s}},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {69--78},
     publisher = {mathdoc},
     volume = {Ser. 9, 10},
     number = {2},
     year = {1999},
     zbl = {1007.60067},
     mrnumber = {516812},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1999_9_10_2_a1/}
}
TY  - JOUR
AU  - Maslowski, Bohdan
AU  - Seidler, Jan
TI  - On sequentially weakly Feller solutions to SPDE’s
JO  - Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
PY  - 1999
SP  - 69
EP  - 78
VL  - 10
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RLIN_1999_9_10_2_a1/
LA  - en
ID  - RLIN_1999_9_10_2_a1
ER  - 
%0 Journal Article
%A Maslowski, Bohdan
%A Seidler, Jan
%T On sequentially weakly Feller solutions to SPDE’s
%J Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
%D 1999
%P 69-78
%V 10
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RLIN_1999_9_10_2_a1/
%G en
%F RLIN_1999_9_10_2_a1
Maslowski, Bohdan; Seidler, Jan. On sequentially weakly Feller solutions to SPDE’s. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 10 (1999) no. 2, pp. 69-78. http://geodesic.mathdoc.fr/item/RLIN_1999_9_10_2_a1/

[1] Z. Brzézniak - D. Gątarek, Martingale solutions and invariant measures for stochastic evolution equations in Banach spaces. The University of Hull, Mathematics Research Reports, 11, 1998, no. 2. | Zbl

[2] R. F. Curtain - A. J. Pritchard, Infinite dimensional linear systems theory. Lecture Notes in Control and Inform. Sci., 8, Springer-Verlag, Berlin 1978. | MR | Zbl

[3] G. Da Prato - D. Gątarek - J. Zabczyk, Invariant measures for semilinear stochastic equations. Stochastic Anal. Appl., 10, 1992, 387-408. | DOI | MR | Zbl

[4] G. Da Prato - J. Zabczyk, Stochastic equations in infinite dimensions. Cambridge University Press, Cambridge 1992. | DOI | MR | Zbl

[5] G. Da Prato - J. Zabczyk, Ergodicity for infinite dimensional systems. Cambridge University Press, Cambridge 1996. | DOI | MR | Zbl

[6] A. Ichikawa, Dynamic programming approach to stochastic evolution equations. SIAM J. Control Optim., 17, 1979, 152-174. | DOI | MR | Zbl

[7] A. Ichikawa, Semilinear stochastic evolution equations: Boundedness, stability and invariant measures. Stochastics, 12, 1984, 1-39. | DOI | MR | Zbl

[8] L. Lecam, Convergence in distribution of stochastic processes. Univ. Calif. Publ. Statist., 2, 1957, 207-236. | MR | Zbl

[9] G. Leha - G. Ritter, Lyapunov-type conditions for stationary distributions of diffusion processes on Hilbert spaces. Stochastics Stochastics Rep., 48, 1994, 195-225. | MR | Zbl

[10] R. Lucchetti - F. Patrone, On Nemytskii’s operator and its application to the lower semicontinuity of integral functionals. Indiana Univ. Math. J., 29, 1980, 703-713. | DOI | MR | Zbl

[11] B. Maslowski - J. Seidler, Probabilistic approach to the strong Feller property. To appear. | DOI | MR | Zbl

[12] J. Seidler - I. Vrkoč, An averaging principle for stochastic evolution equations. Časopis Pěst. Mat., 115, 1990, 240-263. | fulltext EuDML | MR | Zbl

[13] I. Vrkoč, A dynamical system in a Hilbert space with a weakly attractive nonstationary point. Math. Bohem., 118, 1993, 401-423. | fulltext EuDML | MR | Zbl

[14] J. Zabczyk, On optimal stochastic control of discrete-time systems in Hilbert space. SIAM J. Control, 13, 1975, 1217-1234. | MR | Zbl