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Central limit theorem for Hölder processes on m -unit cube

Jana Klicnarová (2007)

Commentationes Mathematicae Universitatis Carolinae

We consider a sequence of stochastic processes ( X n ( 𝐭 ) , 𝐭 [ 0 , 1 ] m ) with continuous trajectories and we show conditions for the tightness of the sequence in the Hölder space with a parameter γ .

Central limit theorem for sampled sums of dependent random variables

Nadine Guillotin-Plantard, Clémentine Prieur (2010)

ESAIM: Probability and Statistics

We prove a central limit theorem for linear triangular arrays under weak dependence conditions. Our result is then applied to dependent random variables sampled by a -valued transient random walk. This extends the results obtained by [N. Guillotin-Plantard and D. Schneider, Stoch. Dynamics3 (2003) 477–497]. An application to parametric estimation by random sampling is also provided.

Cluster continuous time random walks

Agnieszka Jurlewicz, Mark M. Meerschaert, Hans-Peter Scheffler (2011)

Studia Mathematica

In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW model is useful in physics, to model diffusing particles. Its scaling limit is a time-changed process, whose densities solve an anomalous diffusion equation. This paper develops limit theory and governing equations for cluster CTRW, in which a random number of jumps cluster together into a single jump. The clustering introduces a dependence between the waiting times and jumps that significantly affects...

Cogrowth and spectral gap of generic groups

Yann Ollivier (2005)

Annales de l’institut Fourier

The cogrowth exponent of a group controls the random walk spectrum. We prove that for a generic group (in the density model) this exponent is arbitrarily close to that of a free group. Moreover, this exponent is stable under random quotients of torsion-free hyperbolic groups.

Comparing the distributions of sums of independent random vectors

Evgueni I. Gordienko (2005)

Kybernetika

Let ( X n , n 1 ) , ( X ˜ n , n 1 ) be two sequences of i.i.d. random vectors with values in k and S n = X 1 + + X n , S ˜ n = X ˜ 1 + + X ˜ n , n 1 . Assuming that E X 1 = E X ˜ 1 , E | X 1 | 2 < , E | X ˜ 1 | k + 2 < and the existence of a density of X ˜ 1 satisfying the certain conditions we prove the following inequalities: v ( S n , S ˜ n ) c max { v ( X 1 , X ˜ 1 ) , ζ 2 ( X 1 , X ˜ 1 ) } , n = 1 , 2 , , where v and ζ 2 are the total variation and Zolotarev’s metrics, respectively.

Complete q -order moment convergence of moving average processes under ϕ -mixing assumptions

Xing-Cai Zhou, Jin-Guan Lin (2014)

Applications of Mathematics

Let { Y i , - < i < } be a doubly infinite sequence of identically distributed ϕ -mixing random variables, and { a i , - < i < } an absolutely summable sequence of real numbers. We prove the complete q -order moment convergence for the partial sums of moving average processes X n = i = - a i Y i + n , n 1 based on the sequence { Y i , - < i < } of ϕ -mixing random variables under some suitable conditions. These results generalize and complement earlier results.

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