Localization of Unbounded Operators on Guichardet Spaces

Jihong Zhang, Caishi Wang, Lina Tian

School of Mathematics, Lanzhou City University, Lanzhou, Gansu, China.

DOI: 10.4236/jamp.2015.37096                

Abstract

As stochastic gradient and Skorohod integral operators, is an adjoint pair of unbounded operators on Guichardet Spaces. In this paper, we define an adjoint pair of operator , where with being the conditional expectation operator. We show that (resp.) is essentially a kind of localization of the stochastic gradient operators (resp. Skorohod integral operators δ). We examine that and satisfy a local CAR (canonical ani-communication relation) and forms a mutually orthogonal operator sequence although each is not a projection operator. We find that is s-adapted operator if and only if is s-adapted operator. Finally we show application exponential vector formulation of QS calculus.

Keywords

Stochastic Gradient Operator, Skorohod Integral Operator, Localization, Ex-Ponential Vector, Guichardet Spaces

Conflicts of Interest

The authors declare no conflicts of interest.

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