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 (2012)

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? (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.

From almost sure local regularity to almost sure Hausdorff dimension for gaussian fields

Erick Herbin, Benjamin Arras, Geoffroy Barruel (2014)

ESAIM: Probability and Statistics

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Fine regularity of stochastic processes is usually measured in a local way by local Hölder exponents and in a global way by fractal dimensions. In the case of multiparameter Gaussian random fields, Adler proved that these two concepts are connected under the assumption of increment stationarity property. The aim of this paper is to consider the case of Gaussian fields without any stationarity condition. More precisely, we prove that almost surely the Hausdorff dimensions of the range...

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...

Fractional multiplicative processes

Julien Barral, Benoît Mandelbrot (2009)

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

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Statistically self-similar measures on [0, 1] are limit of multiplicative cascades of random weights distributed on the -adic subintervals of [0, 1]. These weights are i.i.d., positive, and of expectation 1/. We extend these cascades naturally by allowing the random weights to take negative values. This yields martingales taking values in the space of continuous functions on [0, 1]. Specifically, we consider for each ∈(0, 1) the martingale ( ) obtained when the weights...

Invariance principles for random walks conditioned to stay positive

Francesco Caravenna, Loïc Chaumont (2008)

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

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Let { be a random walk in the domain of attraction of a stable law 𝒴 , i.e. there exists a sequence of positive real numbers ( ) such that / converges in law to 𝒴 . Our main result is that the rescaled process ( / , ≥0), when conditioned to stay positive, converges in law (in the functional sense) towards the corresponding stable Lévy process conditioned to stay positive. Under some additional assumptions,...

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 fully coupled continuous time random walks

W. Szczotka, P. Żebrowski (2012)

Applicationes Mathematicae

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Continuous time random walks with jump sizes equal to the corresponding waiting times for jumps are considered. Sufficient conditions for the weak convergence of such processes are established and the limiting processes are identified. Furthermore one-dimensional distributions of the limiting processes are given under an additional assumption.

Limit theorem for random walk in weakly dependent random scenery

Nadine Guillotin-Plantard, Clémentine Prieur (2010)

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

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Let =( )≥0 be a random walk on ℤ and =( )∈ℤ a stationary random sequence of centered random variables, independent of . We consider a random walk in random scenery that is the sequence of random variables ( )≥0, where =∑=0 , ∈ℕ. Under a weak dependence assumption on the scenery we prove a functional limit theorem generalizing Kesten and Spitzer’s [ (1979) 5–25]...