To begin with, we assume that the M. C. {x t , tT} is Borel measurable. Using the notation of § 8, we may define a family of random variables {ξ t , tT} on the triple (Δ, Δℱ, P(·|Δ)) as follows:
$${{\xi }_{t}}\left( \omega \right)=\xi \left( t,\omega \right)=x\left( \alpha \left( \omega \right)+t,\omega \right)$$


Markov Process Transition Matrix Conditional Independence Continuous Parameter Lebesgue Measure Zero 
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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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