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Published in:
2011 | OriginalPaper | Chapter
Construction of Markov Processes Associated With Quasi-Regular Dirichlet Forms
Authors : Sergio Albeverio, Ruzong Fan, Frederik Herzberg
Published in: Hyperfinite Dirichlet Forms and Stochastic Processes
Publisher: Springer Berlin Heidelberg
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In this chapter, we consider the construction of tight strong Markov processes associated with standard quasi-regular Dirichlet forms by using the language of nonstandard analysis. In Fan [154], the construction of strong Markov pro- cesses associated with standard symmetric Dirichlet forms was considered. In this chapter, we consider nonsymmetric Dirichlet forms. We consider a standard Dirichlet form (
F
(
·, ·
)
,D
(
F
)) whose state space is a regular Hausdorff space
Y
. We impose conditions directly on the Dirichlet form (
F
(
·, ·
),
D
(
F
)) to obtain associated tight strong Markov processes. The motivation comes from the desire to find the relationship between the family of Dirichlet forms and the family of strong Markov processes.