Approximation of Debuts

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


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.


Markov Process Markov Property Borel Function Finite Measure Pointwise Limit 
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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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