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Tools for Malliavin calculus in UMD Banach spaces
Malliavin calculus Skorohod integral anticipating processes Meyer inequalities UMD Banach space type 2 space chain rule
2012/4/16
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 p...
Infinitely delayed stochastic evolution equations in UMD Banach spaces
stochastic evolution equations UMD Banach spaces
2010/11/18
We prove an existence and uniqueness result for the infinitely delayed stochastic evolution equation $$dU(t) = &\big(AU(t) + F(t,U_t)\big) dt + B(t,U_t)dW_H(t), t\in[0,T_0]$$ where $A$ is the generat...
Decoupling and stochastic integration in UMD Banach spaces
Decoupling stochastic integration' UMD Banach spaces
2009/9/23
Rositiski and Suchanecki have characterized the class of
deterministic E-valued functions integrable with respect to Brownian
motion, where E is a given Banach space. We extend their result to
rand...
A Clark-Ocone formula in UMD Banach spaces
Clark-Ocone formula probability space UMD Banach space
2009/3/19
Let H be a separable real Hilbert space and let F = (Ft)t in [0,T] be the augmented filtration generated by an H-cylindrical Brownian motion WH on [0,T] on a probability space (Ω,F,P). We prove that i...