Viene studiata la regolarità di convoluzioni stocastiche risolvendo un’equazione di Volterra in $\mathbb{R}^{d}$ perturbata da un processo di Wiener spazialmente omogeneo. I risultati generali ottenuti sono applicati a equazioni paraboliche stocastiche con una potenza frazionaria del Laplaciano.
Referenze Bibliografiche
[2]
T. Bojdecki -
L.G. Gorostiza,
Langevin equation for $S^{1}$-valued Gaussian processes and fluctuation limits of infinite particle systems.
Probab. Theory and Related Fields,
73,
1986, 227-244. |
fulltext (doi) |
MR 855224 |
Zbl 0595.60096[4]
T. Bojdecki -
J. Jakubowski,
Stochastic integral for inhomogeneous Wiener process in the dual of a nuclear space.
Journal of Multivariate Analysis,
34,
1990, 185-210. |
fulltext (doi) |
MR 1073105 |
Zbl 0716.60056[5] T. Bojdecki - J. Jakubowski, Stationary distributions for generalized Ornstein-Uhlenbeck processes in conuclear space. Preprint, 1997.
[6]
T. Bojdecki -
J. Jakubowski,
Invariant measures for generalized Langevin equations in conuclear space.
Stochastic Processes and Their Applications,
84,
1999, 1-24. |
fulltext (doi) |
MR 1720095 |
Zbl 0997.60067[8]
Ph. Clément -
G. Da Prato,
White noise perturbation of the heat equation in materials with memory.
Dynamic Systems and Applications,
6,
1997, 441-460. |
MR 1487470 |
Zbl 0893.60035[9]
Ph. Clément -
G. Da Prato -
J. Prüss,
White noise perturbation of the equations of linear parabolic viscoelasticity.
Rendiconti Trieste,
1997. |
Zbl 0911.45010[11]
G. Da Prato -
J. Zabczyk,
Stochastic equations in infinite dimensions.
Encyclopedia of mathematics and its applications, vol.
44,
Cambridge University Press, Cambridge
1992. |
fulltext (doi) |
MR 1207136 |
Zbl 0761.60052[12]
D. Dawson -
G. Gorostiza,
Generalized solutions of a class of nuclear-space-valued stochastic evolution equations.
Appl. Math. Optim.,
22,
1990, 241-263. |
fulltext (doi) |
MR 1068182 |
Zbl 0714.60048[13]
M. Gel'fand -
N. Vilenkin,
Generalized functions 4. Applications of harmonic analysis.
Academic Press, New York
1964. |
Zbl 0144.17202[14]
L. G. Gorostiza -
A. Wakolbinger,
Persistence criteria for a class of critical branching particle systems in continuous time.
The Annals of Probability, No. 1,
19,
1991, 266-288. |
fulltext mini-dml |
MR 1085336 |
Zbl 0732.60093[17]
A. Karczewska -
J. Zabczyk,
A note on stochastic wave equations. Preprint 574, Institute of Mathematics, Polish Academy of Sciences, Warsaw
1997. In:
G. Lumer -
L. Weis (eds.),
Evolution Equations and their Applications in Physical and Life Sciences. Proceedings of the 6th International Conference (Bad Herrenhalb 1998),
Marcel Dekker, to appear. |
MR 1818028 |
Zbl 0978.60066[18]
A. Karczewska -
J. Zabczyk,
Stochastic PDEs with function-valued solutions. Preprint 33, Scuola Normale Superiore di Pisa, Pisa
1997. In:
Ph. Clément -
F. den Hollander -
J. van Neerven -
B. de Pagter (eds.),
Infinite-Dimensional Stochastic Analysis. Proceedings of the Colloquium of the Royal Netherlands Academy of Arts and Sciences (Amsterdam
1999),
North Holland, to appear. |
MR 1832378 |
Zbl 0990.60065[19]
A. Karczewska -
J. Zabczyk,
Regularity of solutions to stochastic Volterra equations. Preprint 17, Scuola Normale Superiore di Pisa, Pisa
1999. |
MR 1841688 |
Zbl 1072.60051[20]
N. S. Landkof,
Foundations of modern potential theory.
Springer-Verlag, Berlin
1972. |
MR 350027 |
Zbl 0253.31001[21]
A. Millet -
P.-L. Morien,
On stochastic wave equation in two space dimensions: regularity of the solution and its density. Preprint 98/9, University Paris 10, Nanterre
1998. |
Zbl 1028.60061[22]
A. Millet -
M. Sanz-Solé,
A stochastic wave equation in two space dimension: smoothness of the law.
The Annals of Probability, to appear. |
fulltext mini-dml |
Zbl 0944.60067[24]
S. Peszat -
J. Zabczyk,
Stochastic evolution equations with a spatially homogeneous Wiener process.
Stochastic Processes Appl.,
72,
1997, 187-204. |
fulltext (doi) |
MR 1486552 |
Zbl 0943.60048[25]
S. Peszat -
J. Zabczyk,
Nonlinear stochastic wave and heat equations. Preprint 584, Institute of Mathematics, Polish Academy of Sciences, Warsaw
1998. |
fulltext (doi) |
MR 1749283 |
Zbl 0959.60044[27]
C. Rovira -
M. Sanz-Solé,
Stochastic Volterra equations in the plane: smoothness of the law. Preprint 226, Universitat de Barcelona
1997. |
Zbl 0991.60052[28]
C. Rovira -
M. Sanz-Solé,
Large deviations for stochastic Volterra equations in the plane. Preprint 233, Universitat de Barcelona
1997. |
Zbl 0983.60010[29]
S. Tindel -
F. Viens,
On space-time regularity for the stochastic heat equation on Lie groups.
Journal of Functional Analysis,
169,
1999, 559-604. |
fulltext (doi) |
MR 1730556 |
Zbl 0953.60046[30]
J. Walsh,
An introduction to stochastic partial differential equations. In:
P. L. Hennequin (ed.),
Ecole d’Eté de Probabilités de Saint-Flour XIV-1984.
Lecture Notes in Math.,
1180,
Springer-Verlag, New York-Berlin
1986, 265-439. |
fulltext (doi) |
MR 876085 |
Zbl 0608.60060