Infinite-dimensional calculus under weak spatial regularity of the processes Journal Article


Author(s): Flandoli, Franco; Russo, Francesco; Zanco, Giovanni
Article Title: Infinite-dimensional calculus under weak spatial regularity of the processes
Affiliation IST Austria
Abstract: Two generalizations of Itô formula to infinite-dimensional 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 path-dependent Itô calculus.
Keywords: Stochastic calculus in Hilbert (Banach) spaces; Itô formula
Journal Title: Journal of Theoretical Probability
ISSN: 0894-9840
Publisher: Springer  
Date Published: 2016-11-25
Start Page: Epub ahead of print
Copyright Statement: CC BY
URL:
DOI: 10.1007/s10959-016-0724-2
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 2014-1607H). 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)
IST Austria Authors
  1. Giovanni Zanco
    1 Zanco
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