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.

Infinite dimensional calculus under weak spatial regularity of the processes / Flandoli, F; Russo, F; Zanco, G. - In: JOURNAL OF THEORETICAL PROBABILITY. - ISSN 0894-9840. - 31:2(2018), pp. 789-826. [10.1007/s10959-016-0724-2]

Infinite dimensional calculus under weak spatial regularity of the processes

Zanco G
2018

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.
Stochastic calculus in Hilbert (Banach) spaces; Itô formula
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/183478
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