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Potential Analysis

, Volume 3, Issue 4, pp 391–422 | Cite as

A study on Markovian maximality, change of probability and regularity

  • Shiqi Song
Article

Abstract

LetE be a rigid separable Banach space andm a bounded Borel measure onE. Let Ext denote the family of all gradient type Dirichlet forms onL2(E, m) such that the domain of their extended generators (cf. Definition 1.1) contain the smooth functions. We prove three results. First, we prove the existence of the maximum element in Ext whenever Ext is not empty. Secondly, let ℰ be the maximum element in Ext (when Ext ≠ Ø) and let φ be a positive function in D(ℰ). We define a new measure μ=φ2·m and we consider the family Extμ associated with the measure μ. We prove that if ℰ is associated with a diffusion process, Extμ is not empty and its maximum element is also associated with a diffusion process. Finally, whenm is a centered Gaussian measure onE, we can prove that Extμ contains exactly one element.

Mathematics Subject Classification (1991)

60J45 

Key words

Dirichlet form Markovian extension regularity of a Dirichlet form generator of a Dirichlet form operator of carré du champ symmetric diffusion process Gaussian measure 

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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Shiqi Song
    • 1
  1. 1.Equipe d'Analyse et ProbabilitésUniversité Evry Val d'Essonne, Boulevard des CoquibusEvry CedexFrance

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