Functionals of Markov processes

  • E. B. Dynkin
Part of the Die Grundlehren der Mathematischen Wissenschaften book series (GL, volume 121/122)

Abstract

Let X = (x t , ζ,ℳ t ,P x ) be a Markov process on the state space (E,ℬ) and let there correspond to each ω ∈ Ω some intervall I (ω) on the half line [0, ∞). The function
$$\varphi = \varphi _t^8(\omega )\quad (s\underline \leqslant t \in I(\omega )),$$
taking values in some measurable space (Ẽ,ℬ) is called a functional of the Markov process X, if the following condition is satisfied:

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Copyright information

© Springer-Verlag Berlin · Göttingen · Heidelberg 1965

Authors and Affiliations

  • E. B. Dynkin
    • 1
  1. 1.University of MoscowRussia

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