Tools for Malliavin Calculus in UMD Banach Spaces

被引：0
作者：
Matthijs Pronk
Mark Veraar
机构：
[1] Delft University of Technology,Delft Institute of Applied Mathematics
来源：
Potential Analysis | 2014年 / 40卷
关键词：
Malliavin calculus; Skorohod integral; Anticipating processes; Meyer inequalities; UMD Banach space; Type 2 space; Chain rule; Itô formula; 60H07; 60B11; 60H05;
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学科分类号：
摘要：
In this paper we study the Malliavin derivatives and Skorohod integrals for processes taking values in an infinite dimensional space. Such results are motivated by their applications to SPDEs and in particular financial mathematics. Vector-valued Malliavin theory in Banach space E is naturally restricted to spaces E which have the so-called umd property, which arises in harmonic analysis and stochastic integration theory. We provide several new results and tools for the Malliavin derivatives and Skorohod integrals in an infinite dimensional setting. In particular, we prove weak characterizations, a chain rule for Lipschitz functions, a sufficient condition for pathwise continuity and an Itô formula for non-adapted processes.
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页码：307 / 344
页数：37
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