Time-changes of self-similar Markov processes
J. Vuolle-Apiala (1989)
Annales de l'I.H.P. Probabilités et statistiques
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J. Vuolle-Apiala (1989)
Annales de l'I.H.P. Probabilités et statistiques
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W. Bołt, A. A. Majewski, T. Szarek (2012)
Studia Mathematica
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Strassen's invariance principle for additive functionals of Markov chains with spectral gap in the Wasserstein metric is proved.
Maria Jankiewicz, T. Rolski (1977)
Applicationes Mathematicae
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W. P. Cherry, R. L. Disney (1983)
Applicationes Mathematicae
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Christian Paroissin, Bernard Ycart (2010)
ESAIM: Probability and Statistics
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A sample of i.i.d. continuous time Markov chains being defined, the sum over each component of a real function of the state is considered. For this functional, a central limit theorem for the first hitting time of a prescribed level is proved. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications.
Masao Nagasawa (1972)
Séminaire de probabilités de Strasbourg
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Maria Jankiewicz (1978)
Applicationes Mathematicae
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Cristina Gzyl, Henryk Gzyl (1979)
Annales de l'I.H.P. Probabilités et statistiques
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Evgeny B. Dynkin (1975)
Annales de l'institut Fourier
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Intuitively, an additive functional of a stochastic process gives a method to measure time taking into account the development of the process. We associate with any set of states the mathematical expectation of time belongs to . In this way, we establish to one-to-one correspondence between all the normal additive functionals of a Markov process and all the -finite measures on the state space which charge no inaccessible set. This is proved under the condition that transition...
R. Magiera, R. Różanski (1985)
Banach Center Publications
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