Regularity results for infinite dimensional diffusions. A Malliavin calculus approach
Stefano Bonaccorsi; Marco Fuhrman
- Volume: 10, Issue: 1, page 35-45
- ISSN: 1120-6330
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topBonaccorsi, Stefano, and Fuhrman, Marco. "Regularity results for infinite dimensional diffusions. A Malliavin calculus approach." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 10.1 (1999): 35-45. <http://eudml.org/doc/252435>.
@article{Bonaccorsi1999,
abstract = {We prove some smoothing properties for the transition semigroup associated to a nonlinear stochastic equation in a Hilbert space. The proof introduces some tools from the Malliavin calculus and is based on a integration by parts formula.},
author = {Bonaccorsi, Stefano, Fuhrman, Marco},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Transition semigroups; Strong Feller property; Logarithmic derivative; Malliavin calculus; transition semigroup; strong Feller property},
language = {eng},
month = {3},
number = {1},
pages = {35-45},
publisher = {Accademia Nazionale dei Lincei},
title = {Regularity results for infinite dimensional diffusions. A Malliavin calculus approach},
url = {http://eudml.org/doc/252435},
volume = {10},
year = {1999},
}
TY - JOUR
AU - Bonaccorsi, Stefano
AU - Fuhrman, Marco
TI - Regularity results for infinite dimensional diffusions. A Malliavin calculus approach
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1999/3//
PB - Accademia Nazionale dei Lincei
VL - 10
IS - 1
SP - 35
EP - 45
AB - We prove some smoothing properties for the transition semigroup associated to a nonlinear stochastic equation in a Hilbert space. The proof introduces some tools from the Malliavin calculus and is based on a integration by parts formula.
LA - eng
KW - Transition semigroups; Strong Feller property; Logarithmic derivative; Malliavin calculus; transition semigroup; strong Feller property
UR - http://eudml.org/doc/252435
ER -
References
top- Bonaccorsi, S., Some applications in Malliavin calculus. Ph. D. thesis, Università degli Studi di Trento, 1998.
- Da Prato, G. - Zabczyk, J., Stochastic equations in infinite dimensions. In: Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge1992. Zbl0761.60052MR1207136DOI10.1017/CBO9780511666223
- Da Prato, G. - Zabczyk, J., Ergodicity for infinite-dimensional systems. In: London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge1996. Zbl0849.60052MR1417491DOI10.1017/CBO9780511662829
- Fuhrman, M., Smoothing properties of nonlinear stochastic equations in Hilbert spaces. NoDEA Nonlinear Differential Equations Appl., 3(4), 1996, 445-464. Zbl0866.60050MR1418590DOI10.1007/BF01193830
- Grorud, A. - Pardoux, É., Intégrales hilbertiennes anticipantes par rapport à un processus de Wiener cylindrique et calcul stochastique associé. Appl. Math. Optim., 25 (1), 1992, 31-49. Zbl0754.60051MR1133251DOI10.1007/BF01184155
- Nualart, D., The Malliavin calculus and related topics. Probability and its Applications, Springer-Verlag, New York1995. Zbl0837.60050MR1344217
- Peszat, S. - Zabczyk, J., Strong Feller property and irreducibility for diffusions on Hilbert spaces. Ann. Probab., 23 (1), 1995, 157-172. Zbl0831.60083MR1330765
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