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Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35) by Zhenqing Chen, Masatoshi Fukushima

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Appendix A

 

ESSENTIALS OF MARKOV PROCESSES

A.1. MARKOV PROCESSES

In this section, we introduce various concepts of Markov processes, such as the Markov process, right process, standard process, and Hunt process.

A.1.1. Preliminaries

In this subsection, we collect some preliminaries for Sections A.1, A.2, and A.3. Let Ω be a set. A class M of subsets of Ω is called a σ-field if Ω ∈ M and it is closed under the operations of taking a countable union and complement. The couple (Ω, M) is said to be a measurable space in this case. Given a measurable space (Ω, M) and a subset image of Ω, the trace of M on is defined by and denoted by is then a measurable ...

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