Infinite-dimensional calculus under weak spatial regularity of the processes
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.
31
2
789-826
789-826
Springer
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