STOCHASTIC-EVOLUTION EQUATIONS WITH RANDOM GENERATORS

Authors
LEON JA NUALART D
Citation
Ja. Leon et D. Nualart, STOCHASTIC-EVOLUTION EQUATIONS WITH RANDOM GENERATORS, Annals of probability, 26(1), 1998, pp. 149-186
Citations number
16
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Annals of probability → ACNP
ISSN journal
00911798
Volume
26
Issue
1
Year of publication
1998
Pages
149 - 186
Database
ISI
SICI code
0091-1798(1998)26:1<149:SEWRG>2.0.ZU;2-C
Abstract
We prove the existence of a unique mild solution for a stochastic evol ution equation on a Hilbert space driven by a cylindrical Wiener proce ss. The generator of the corresponding evolution system is supposed to be random and adapted to the filtration generated by the Wiener proce ss. The proof is based on a maximal inequality for the Skorohod integr al deduced from the Ito's formula for this anticipating stochastic int egral.