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

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  • Razafimanantena, Edouard A.

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.

Suggested Citation

  • Razafimanantena, Edouard A., 1991. "Construction of a general class of Dirichlet forms in terms of white noise analysis," Stochastic Processes and their Applications, Elsevier, vol. 39(2), pages 263-276, December.
  • Handle: RePEc:eee:spapps:v:39:y:1991:i:2:p:263-276
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