Rectificatif demandé par l'auteur

E. B. Dynkin

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On the functional equation f(x+y) =f(x) +f(y)

H. Kestelman (1947)

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Continuous extensions of spectral measures

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Additive functionals of Markov processes and stochastic systems

Evgeny B. Dynkin (1975)

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Intuitively, an additive functional of a stochastic process $(x_{t}, P)$ gives a method to measure time taking into account the development of the process. We associate with any set of states $C$ the mathematical expectation of time $x_{t}$ belongs to $C$ . In this way, we establish to one-to-one correspondence between all the normal additive functionals of a Markov process and all the $δ$ -finite measures on the state space which charge no inaccessible set. This is proved under the condition that transition...