The research on the strong Markov property

Tang Rong, Huang Yonghui

Abstract


Let X(t, ω) = {xt(ω): t ≥ 0} be a Markov process defined on a probability space (Ω,F, P) and valued in a measurable space (E; E ). In this paper, we give the definitions of σ-algebras prior to α and post-α and discuss their properties. At the same time, we prove that the strong Markov property holds for an arbitrary Markov process, that is, we prove that the Markov property is equivalent to the strong Markov property.

Keywords


σ-algebra prior to α, σ-algebra post-α; Markov property; the strong Markov property; stopping time; homogeneity

Mathematics Subject Classification


60J25, 60J27

References


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