Construction of a general class of Dirichlet forms in terms of white noise analysis

Edouard A. Razafimanantena

Stochastic Processes and their Applications, 1991, vol. 39, issue 2, 263-276

Abstract: In the framework of white noise analysis a Gel'fand triple has been defined (e.g. Kubo and Yokoi, 1989), the space of smooth test functionals () and the space of Hida distributions ()* play some important roles. It has been shown (e.g. Yokoi, 1990) that a positive Hida distribution [Phi] is given by a positive measure [nu][Phi] on the space of real tempered distributions *. Thus the space (L2)[Phi][triple bond; length as m-dash]L2(*; , [nu][Phi]) can be defined, where is the Borel [sigma]-algebra on * generated by the weak topology. The present article is concerned with a special choice of pre-Dirichlet forms with domain () on (L2)[Phi] which is a generalization of the energy form (Hida, Potthoff and Streit, 1988) and of the type , for each F[epsilon]() and where (Hj,k; j, k[epsilon]0) is a double sequence of test functionals satisfying some natural conditions. Some closability results are given in the last section under mild conditions.

Keywords: Dirichlet; forms; closable; forms; white; noise; test; functionals; Hida; distributions; directional; derivative; second; quantization (search for similar items in EconPapers)
Date: 1991
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