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Displaying similar documents to “A note on occupation times of stationary processes.”

Induced stationary process and structure of locally square integrable periodically correlated processes

Andrzej Makagon (1999)

Studia Mathematica

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A one-to-one correspondence between locally square integrable periodically correlated (PC) processes and a certain class of infinite-dimensional stationary processes is obtained. The correspondence complements and clarifies Gladyshev's known result [3] describing the correlation function of a continuous periodically correlated process. In contrast to Gladyshev's paper, the procedure for explicit reconstruction of one process from the other is provided. A representation of a PC process...

Long memory and self-similar processes

Gennady Samorodnitsky (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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This paper is a survey of both classical and new results and ideas on long memory, scaling and self-similarity, both in the light-tailed and heavy-tailed cases.

Process-level large deviations for nonlinear Hawkes point processes

Lingjiong Zhu (2014)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has an explicit formula.