Displaying similar documents to “Random fractals generated by a local Gaussian process indexed by a class of functions”

Random fractals generated by a local gaussian process indexed by a class of functions

Claire Coiffard (2011)

ESAIM: Probability and Statistics

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In this paper, we extend the results of Orey and Taylor [S. Orey and S.J. Taylor, How often on a Brownian path does the law of the iterated logarithm fail? 28 (1974) 174–192] relative to random fractals generated by oscillations of Wiener processes to a multivariate framework. We consider a setup where Gaussian processes are indexed by classes of functions.

Large deviations for directed percolation on a thin rectangle

Jean-Paul Ibrahim (2012)

ESAIM: Probability and Statistics

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Following the recent investigations of Baik and Suidan in [(2005) 325–337] and Bodineau and Martin in [ (2005) 105–112 (electronic)], we prove large deviation properties for a last-passage percolation model in ℤ whose paths are close to the axis. The results are mainly obtained when the random weights are Gaussian or have a finite moment-generating function and rely, as in [J. Baik and T.M. Suidan, (2005) 325–337] and [T. Bodineau and J. Martin, ...

On harmonic functions of symmetric Lévy processes

Ante Mimica (2014)

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

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We consider some classes of Lévy processes for which the estimate of Krylov and Safonov (as in ( (2002) 375–388)) fails and thus it is not possible to use the standard iteration technique to obtain a-priori Hölder continuity estimates of harmonic functions. Despite the failure of this method, we obtain some a-priori regularity estimates of harmonic functions for these processes. Moreover, we extend results from ( (2006) 547–575) and obtain asymptotic behavior...

Connectivity bounds for the vacant set of random interlacements

Vladas Sidoravicius, Alain-Sol Sznitman (2010)

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

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The model of random interlacements on ℤ, ≥3, was recently introduced in [Vacant set of random interlacements and percolation. Available at http://www.math.ethz.ch/u/sznitman/preprints]. A non-negative parameter parametrizes the density of random interlacements on ℤ. In the present note we investigate connectivity properties of the vacant set left by random interlacements at level , in the non-percolative regime >∗, with ∗ the non-degenerate critical parameter for the percolation...

On the Brunk-Chung type strong law of large numbers for sequences of blockwise -dependent random variables

Le Van Thanh (2006)

ESAIM: Probability and Statistics

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For a sequence of blockwise -dependent random variables {≥ 1}, conditions are provided under which lim n → ∞ ( ∑ i = 1 n X i ) / b n = 0 almost surely where {≥ 1} is a sequence of positive constants. The results are new even when . As special case, the Brunk-Chung strong law of large numbers is obtained for sequences of independent random variables. The current work also extends results of Móricz [ (1987) 709–715], and Gaposhkin [. (1994) 804–812]. The sharpness of the results is illustrated by examples. ...

Wiener integral for the coordinate process under the -finite measure unifying Brownian penalisations

Kouji Yano (2011)

ESAIM: Probability and Statistics

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Wiener integral for the coordinate process is defined under the -finite measure unifying Brownian penalisations, which has been introduced by [Najnudel , (2007) 459–466] and [Najnudel , . Mathematical Society of Japan, Tokyo (2009)]. Its decomposition before and after last exit time from 0 is studied. This study prepares for the author's recent study [K. Yano, (2010) 3492–3516] of Cameron-Martin formula for the -finite measure. ...

Sojourn time in ℤ for the Bernoulli random walk on ℤ

Aimé Lachal (2012)

ESAIM: Probability and Statistics

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Let (Sk)k≥1 be the classical Bernoulli random walk on the integer line with jump parameters p ∈ (0,1) and q = 1 − p. The probability distribution of the sojourn time of the walk in the set of non-negative integers up to a fixed time is well-known, but its expression is not simple. By modifying slightly...

Properties of local-nondeterminism of Gaussian and stable random fields and their applications

Yimin Xiao (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this survey, we first review various forms of local nondeterminism and sectorial local nondeterminism of Gaussian and stable random fields. Then we give sufficient conditions for Gaussian random fields with stationary increments to be strongly locally nondeterministic (SLND). Finally, we show some applications of SLND in studying sample path properties of ( N , d ) -Gaussian random fields. The class of random fields to which the results are applicable includes fractional Brownian motion, the...

A branching-selection process related to censored Galton–Walton processes

Olivier Couronné, Lucas Gerin (2014)

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

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We obtain the asymptotics for the speed of a particular case of a particle system with branching and selection introduced by Bérard and Gouéré [ (2010) 323–342]. The proof is based on a connection with a supercritical Galton–Watson process at a certain level.