Transition functions, corresponding to almost multiplicative functionals

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

Abstract

A functional of α=α t 8 (stI(ω)) of a Markov process X taking values in the interval [0,+∞) is said to be multiplicative if a set of full measure \(\tilde \Omega \) can be found such that for each \(\omega \in \tilde \Omega \)
$$\alpha _t^8(\omega )\alpha _u^t(\omega ) = \alpha _u^8(\omega )$$
(9.1)
for all stuI(ω). A functional α is said to be almost multiplicative, if for any 0≦stu, xE
$$\alpha _t^8\alpha _u^t = \alpha _u^8\quad (a.s.\Omega _u^8,{P_x}).$$
(9.2)

Keywords

Dition 

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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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