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

State Space Markov Process Transition Function Wiener Process Nonnegative Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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