Author(s):

Flandoli, Franco; Russo, Francesco; Zanco, Giovanni

Article Title: 
Infinitedimensional calculus under weak spatial regularity of the processes

Affiliation 
IST Austria 
Abstract: 
Two generalizations of Itô formula to infinitedimensional spaces are given.
The first one, in Hilbert spaces, extends the classical one by taking advantage of
cancellations when they occur in examples and it is applied to the case of a group
generator. The second one, based on the previous one and a limit procedure, is an Itô
formula in a special class of Banach spaces having a product structure with the noise
in a Hilbert component; again the key point is the extension due to a cancellation. This
extension to Banach spaces and in particular the specific cancellation are motivated
by pathdependent Itô calculus.

Keywords: 
Stochastic calculus in Hilbert (Banach) spaces; Itô formula

Journal Title:

Journal of Theoretical Probability

ISSN:

08949840

Publisher:

Springer

Date Published:

20161125

Start Page: 
Epub ahead of print

Copyright Statement: 
CC BY

URL: 

DOI: 
10.1007/s1095901607242

Notes: 
Open access funding provided by Institute of Science and Technology (IST Austria). The second named author benefited partially from the support of the “FMJH Program Gaspard Monge in Optimization and Operations Research” (Project 20141607H). He is also grateful for the invitation to the Department of Mathematics of the University of Pisa. The third named author is grateful for the invitation to ENSTA.

Open access: 
yes (OA journal) 