From now on we assume that the minimal state space I of the M. C. {x t , tT} is discrete and that it is compactified to \( \bar{I} \) by adjoining the fictitious state ∞. We also assume that the transition matrix (p ij )is standard. Instead of going at once to a well-separable and measurable version as guaranteed by Theorem 4.3, we shall first investigate separately the consequences of separability and measurability. In this and the next two sections a theorem which is proved under the further assumption of separability is marked with (S), that of measurability with (M), that of both with (SM).


Transition Matrix Open Interval Continuous Parameter Sample Function Strong Markov Property 
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Copyright information

© Springer-Verlag OHG. Berlin · Göttingen · Heidelberg 1960

Authors and Affiliations

  • Kai Lai Chung
    • 1
  1. 1.Syracuse UniversityUSA

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