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An algebraic approach to Pólya processes

Nicolas Pouyanne (2008)

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

Pólya processes are natural generalizations of Pólya–Eggenberger urn models. This article presents a new approach of their asymptotic behaviour via moments, based on the spectral decomposition of a suitable finite difference transition operator on polynomial functions. Especially, it provides new results for large processes (a Pólya process is called small when 1 is a simple eigenvalue of its replacement matrix and when any other eigenvalue has a real part ≤1/2; otherwise, it is called large).

An almost sure invariance principle for renormalized intersection local times.

Bass, Richard F., Rosen, Jay (2005)

Electronic Journal of Probability [electronic only]

An almost sure limit theorem for $α$ -mixing random fields.

Tómács, Tibor (2008)

Annales Mathematicae et Informaticae

An extension of a result of Csiszár.

Cerrito, P.B. (1986)

International Journal of Mathematics and Mathematical Sciences

An infinite dimensional central limit theorem for correlated martingales

Ilie Grigorescu (2004)

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

An invariance principle for Azéma martingales

Nathanaël Enriquez (2007)

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

An invariance principle for Markov processes and brownian particles with singular interaction

Hirofumi Osada (1998)

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

An Invariance Principle for Progressively Truncated Likelihood Ratio Statistics.

P.K. Sen, Y. Tsong (1981)

Metrika

An Invariance Principle for Reduced U-Statistics.

N. Herrndorf (1986)

Metrika

An invariance principle for the law of the iterated logarithm for some Markov chains

W. Bołt, A. A. Majewski, T. Szarek (2012)

Studia Mathematica

Strassen's invariance principle for additive functionals of Markov chains with spectral gap in the Wasserstein metric is proved.

An Invariance Principle for U-Statistics in Simple Random Sampling without Replacement.

H. Milbrodt (1987)

Metrika

An invariance principle in $L^{2} [0, 1]$ for non stationary $ϕ$ -mixing sequences

Paulo Eduardo Oliveira, Charles Suquet (1995)

Commentationes Mathematicae Universitatis Carolinae

Invariance principle in $L^{2} (0, 1)$ is studied using signed random measures. This approach to the problem uses an explicit isometry between $L^{2} (0, 1)$ and a reproducing kernel Hilbert space giving a very convenient setting for the study of compactness and convergence of the sequence of Donsker functions. As an application, we prove a $L^{2} (0, 1)$ version of the invariance principle in the case of $ϕ$ -mixing random variables. Our result is not available in the $D (0, 1)$ -setting.

An $L^{2} [0, 1]$ invariance principle for LPQD random variables.

Oliveira, P.E., Suquet, Ch. (1996)

Portugaliae Mathematica

Antisymmetric functionals of reversible Markov processes

Sheldon Goldstein (1995)

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

Approximation in law to the d-parameter fractional Brownian sheet based on the functional invariance principle.

Xavier Bardina, Carme Florit (2005)

Revista Matemática Iberoamericana

We show a result of approximation in law of the d-parameter fractional Brownian sheet in the space of the continuous functions on [0,T]d. The construction of these approximations is based on the functional invariance principle.

Approximation of predictable characteristics of processes with filtrations

Leszek Slominski (1987)

Séminaire de probabilités de Strasbourg

Approximations for the maximum of stochastic processes with drift

István Berkes, Lajos Horváth (2003)

Kybernetika

If a stochastic process can be approximated with a Wiener process with positive drift, then its maximum also can be approximated with a Wiener process with positive drift.

Asymptotic distribution of coordinates on high dimensional spheres.

Spruill, Marcus C. (2007)

Electronic Communications in Probability [electronic only]

Asymptotic properties of power variations of Lévy processes

Jean Jacod (2007)

ESAIM: Probability and Statistics

We determine the asymptotic behavior of the realized power variations, and more generally of sums of a given function f evaluated at the increments of a Lévy process between the successive times iΔn for i = 0,1,...,n. One can elucidate completely the first order behavior, that is the convergence in probability of such sums, possibly after normalization and/or centering: it turns out that there is a rather wide variety of possible behaviors, depending on the structure of jumps and on the chosen...

Asymptotics for general nonstationary fractionally integrated processes without prehistoric influence.

Wang, Qiying, Lin, Yan-Xia, Gulati, Chandra (2002)

Journal of Applied Mathematics and Decision Sciences

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