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Published in:
2011 | OriginalPaper | Chapter
Standard Representation Theory
Authors : Sergio Albeverio, Ruzong Fan, Frederik Herzberg
Published in: Hyperfinite Dirichlet Forms and Stochastic Processes
Publisher: Springer Berlin Heidelberg
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The purpose of this chapter is to study the standard projection of hyperfinite Markov chains, and the standard projection of hyperfinite Markov chains associated with hyperfinite quadratic forms. At first, we shall introduce in Sect. 3.1 a concept of irregularity; and then we shall prove that if a hyperfinite Markov chain
X
(·,
t
) has a set of irregularities, its standard part
x
(·,
t
) is a strong Markov process. In Sect. 3.2, we shall find conditions on hyperfinite quadratic forms which guarantee that the modified standard parts of associated hyperfinite Markov chains are strong Markov processes.