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Additive functionals of Markov processes and stochastic systems

Evgeny B. Dynkin — 1975

Annales de l'institut Fourier

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 probabilities...

Martin boundary and positive solutions of some boundary value problems

Evgeny B. Dynkin — 1965

Annales de l'institut Fourier

Nous étudions le problème de Neumann avec dérivée oblique dans un domaine 2-dimensionnel borné par un contour régulier C . Le champ vectoriel donné sur C peut être tangent à C en un nombre fini de points. En utilisant une extension de la méthode de Martin nous trouvons toutes les solutions positives de ce problème aux valeurs limites.

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