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Approximation of Debuts

  • Neil Falkner
Part of the Progress in Probability and Statistics book series (PRPR, volume 7)

Abstract

Consider a Markov process X whose state space is an arbitrary measurable space not endowed with any topology to begin with. Assume only that X has no branch points and that for each a-excessive function f, the process (f(Xt)) is a.s. right continuous. Let εe be the σ-field generated by the a-excessive functions. We show that for each A ∈ εe and each finite measure u on the state space, there is a decreasing sequence (Gn) of finely open, εe-measurable supersets of A such that \( {{\text{D}}_{{{\text{G}}_{\text{n}}}}} \uparrow {{\text{D}}_{\text{A}}} \) Pµ-a.s. We deduce this result from a similar one which applies also to suitable non-Markov processes.

Keywords

Markov Process Markov Property Borel Function Finite Measure Pointwise Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston, Inc. 1984

Authors and Affiliations

  • Neil Falkner
    • 1
  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA

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