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To establish lists of words with unexpected frequencies in long sequences, for instance in a molecular biology context, one needs to quantify the exceptionality of families of word frequencies in random sequences. To this aim, we study large deviation probabilities of multidimensional word counts for Markov and hidden Markov models. More specifically, we compute local Edgeworth expansions of arbitrary degrees for multivariate partial sums of lattice valued functionals of finite Markov...

Large deviations for local times of stable processes and stable random walks in 1 dimension.

Chen, Xia, Li, Wenbo V., Rosen, Jay (2005)

Electronic Journal of Probability [electronic only]

Large favourite sites of simple random walk and the Wiener process.

Csáki, Endre, Shi, Zhan (1998)

Electronic Journal of Probability [electronic only]

Laws of the iterated logarithm for the local times of recurrent random walks on Z2 and of Lévy processes and Random walks in the domain of attraction of Cauchy random variables

Michael B. Marcus, Jay Rosen (1994)

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

Le drap brownien comme limite en loi des temps locaux linéaires

Marc Yor (1983)

Séminaire de probabilités de Strasbourg

Le mouvement brownien de Lévy indexé par $ℝ^{3}$ comme limite centrale de temps locaux d’intersection

Sophie Weinryb, Marc Yor (1988)

Séminaire de probabilités de Strasbourg

Le problème de Skorokhod sur $ℝ$ : une approche avec le temps local

Pierre Vallois (1983)

Séminaire de probabilités de Strasbourg

Le support exact du temps local d'une martingale continue

Maurizio Pratelli (1979)

Séminaire de probabilités de Strasbourg

Les changements de temps en théorie générale des processus

Nicole El Karoui, Paul-André Meyer (1977)

Séminaire de probabilités de Strasbourg

Les travaux d'Azéma sur le retournement du temps

Paul-André Meyer (1974)

Séminaire de probabilités de Strasbourg

Lévy classes and self-normalization.

Khoshnevisan, Davar (1996)

Electronic Journal of Probability [electronic only]

Limit theorems and variation properties for fractional derivatives of the local time of a stable process

P. J. Fitzsimmons, R. K. Getoor (1992)

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

Limit theorems for some functionals with heavy tails of a discrete time Markov chain

Patrick Cattiaux, Mawaki Manou-Abi (2014)

ESAIM: Probability and Statistics

Consider an irreducible, aperiodic and positive recurrent discrete time Markov chain (Xn,n ≥ 0) with invariant distribution μ. We shall investigate the long time behaviour of some functionals of the chain, in particular the additive functional $S_{n} = \sum_{i = 1}^{n} f (X_{i})$ S n = ∑ i = 1 n f ( X i ) for a possibly non square integrable functionf. To this end we shall link ergodic properties of the chain to mixing properties, extending known results in the continuous time case. We will then use existing results of convergence...

Limit theorems for stationary Markov processes with L2-spectral gap

Déborah Ferré, Loïc Hervé, James Ledoux (2012)

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

Let ${(X_{t}, Y_{t})}_{t \in 𝕋}$ be a discrete or continuous-time Markov process with state space $𝕏 \times ℝ^{d}$ where $𝕏$ is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. ${(X_{t}, Y_{t})}_{t \in 𝕋}$ is assumed to be a Markov additive process. In particular, this implies that the first component ${(X_{t})}_{t \in 𝕋}$ is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process ${(Y_{t})}_{t \in 𝕋}$ is shown to satisfy the...

Linear modulus of a multidimensional semigroup of $L_{1}$ -contractions and a differentiation theorem

Dogan Çömez (1989)

Colloquium Mathematicae

Local behaviour of local times of super-brownian motion

Mathieu Merle (2006)

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

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