Occupation time sets of supports of continuous additive functionals
Cristina Gzyl, Henryk Gzyl (1979)
Annales de l'I.H.P. Probabilités et statistiques
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Cristina Gzyl, Henryk Gzyl (1979)
Annales de l'I.H.P. Probabilités et statistiques
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Jozef Nagy (1968)
Časopis pro pěstování matematiky
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Vladas Pipiras, Murad S. Taqqu (2008)
Annales de l'I.H.P. Probabilités et statistiques
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We consider an important subclass of self-similar, non-gaussian stable processes with stationary increments known as self-similar stable mixed moving averages. As previously shown by the authors, following the seminal approach of Jan Rosiński, these processes can be related to nonsingular flows through their minimal representations. Different types of flows give rise to different classes of self-similar mixed moving averages, and to corresponding general decompositions of these processes....
R. Émilion (1985)
Annales de l'I.H.P. Probabilités et statistiques
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C.-S. Lin, Y.J. Cho (1997)
Publications de l'Institut Mathématique
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Ken R. Duffy, Claudio Macci, Giovanni Luca Torrisi (2011)
ESAIM: Probability and Statistics
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We prove that the large deviation principle holds for a class of processes inspired by semi-Markov additive processes. For the processes we consider, the sojourn times in the phase process need not be independent and identically distributed. Moreover the state selection process need not be independent of the sojourn times. We assume that the phase process takes values in a finite set and that the order in which elements in the set, called states, are visited is selected stochastically....
Ken R. Duffy, Claudio Macci, Giovanni Luca Torrisi (2012)
ESAIM: Probability and Statistics
Similarity:
We prove that the large deviation principle holds for a class of processes inspired by semi-Markov additive processes. For the processes we consider, the sojourn times in the phase process need not be independent and identically distributed. Moreover the state selection process need not be independent of the sojourn times. We assume that the phase process takes values in a finite set and that the order in which elements in the set, called states, are visited is selected stochastically....