The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Tail fields generated by symbol counts in measure-preserving systems”

Epsilon-independence between two processes

Tomasz Downarowicz, Paulina Grzegorek (2008)

Studia Mathematica

Similarity:

We study the notion of ε-independence of a process on finitely (or countably) many states and that of ε-independence between two processes defined on the same measure preserving transformation. For that we use the language of entropy. First we demonstrate that if a process is ε-independent then its ε-independence from another process can be verified using a simplified condition. The main direction of our study is to find natural examples of ε-independence. In case of ε-independence of...

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.

Spontaneous clustering in theoretical and some empirical stationary processes

T. Downarowicz, Y. Lacroix, D. Léandri (2010)

ESAIM: Probability and Statistics

Similarity:

In a stationary ergodic process, clustering is defined as the tendency of events to appear in series of increased frequency separated by longer breaks. Such behavior, contradicting the theoretical “unbiased behavior” with exponential distribution of the gaps between appearances, is commonly observed in experimental processes and often difficult to explain. In the last section we relate one such empirical example of clustering, in the area of marine technology. In the theoretical part...

On small deviations of Gaussian processes using majorizing measures

Michel J. G. Weber (2012)

Colloquium Mathematicae

Similarity:

We give two examples of periodic Gaussian processes, having entropy numbers of exactly the same order but radically different small deviations. Our construction is based on Knopp's classical result yielding existence of continuous nowhere differentiable functions, and more precisely on Loud's functions. We also obtain a general lower bound for small deviations using the majorizing measure method. We show by examples that our bound is sharp. We also apply it to Gaussian independent sequences...

Excursions of the integral of the brownian motion

Emmanuel Jacob (2010)

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

Similarity:

The integrated brownian motion is sometimes known as the Langevin process. Lachal studied several excursion laws induced by the latter. Here we follow a different point of view developed by Pitman for general stationary processes. We first construct a stationary Langevin process and then determine explicitly its stationary excursion measure. This is then used to provide new descriptions of Itô’s excursion measure of the Langevin process reflected at a completely inelastic boundary, which...

Alpha-stable branching and beta-coalescents.

Birkner, Matthias, Blath, Jochen, Capaldo, Marcella, Etheridge, Alison M., Möhle, Martin, Schweinsberg, Jason, Wakolbinger, Anton (2005)

Electronic Journal of Probability [electronic only]

Similarity: