Infinite-dimensional calculus under weak spatial regularity of the processes

Franco Flandoli, Giovanni Zanco and Francesco Russo
to appear
Publication type:
Paper in peer-reviewed journals
Journal of Theoretical Probability
images/icons/icon_arxiv.png 1511.05744
Keywords :
Stochastic calculus in Hilbert (Banach) spaces; Itô formula
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 Hilbertian 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.
    author={Franco Flandoli and Giovanni Zanco and Francesco Russo },
    title={Infinite-dimensional calculus under weak spatial regularity of 
           the processes },
    journal={Journal of Theoretical Probability },
    year={to appear },