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

Claire Coiffard (2012)

ESAIM: Probability and Statistics

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? Proc. London Math. Soc.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.

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

Claire Coiffard (2011)

ESAIM: Probability and Statistics

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? Proc. London Math. Soc. 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.

Random paths with bounded local time

Itai Benjamini, Nathanaël Berestycki (2010)

Journal of the European Mathematical Society

We consider one-dimensional Brownian motion conditioned (in a suitable sense) to have a local time at every point and at every moment bounded by some fixed constant. Our main result shows that a phenomenon of entropic repulsion occurs: that is, this process is ballistic and has an asymptotic velocity approximately 4.58... as high as required by the conditioning (the exact value of this constant involves the first zero of a Bessel function). We also study the random walk case and show that the process...

Random walk on a building of type Ãr and brownian motion of the Weyl chamber

Bruno Schapira (2009)

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

In this paper we study a random walk on an affine building of type Ãr, whose radial part, when suitably normalized, converges toward the brownian motion of the Weyl chamber. This gives a new discrete approximation of this process, alternative to the one of Biane (Probab. Theory Related Fields89 (1991) 117–129). This extends also the link at the probabilistic level between riemannian symmetric spaces of the noncompact type and their discrete counterpart, which had been previously discovered by Bougerol...

Recorridos aleatorios simples en tiempo continuo.

Ricardo Vélez Ibarrola (1983)

Trabajos de Estadística e Investigación Operativa

The properties of a certain generalization of simple random walk to continuous time are analyzed in this paper. After the definition, its transition probabilities, and the differential equations satisfied by those, are obtained. Under some conditions, the convergence of this random walk to a Wiener process is then established. Finally, absorption probabilities and mean times until absorption are calculated, giving some insight into the behaviour of the process.

Régularité Besov-Orlicz du temps local Brownien

Yue Hu, Mohamed Mellouk (2000)

Studia Mathematica

Let ( B t , t ∈ [ 0 , 1 ] ) be a linear Brownian motion starting from 0 and denote by ( L t ( x ) , t ≥ 0 , x ∈ ℝ ) its local time. We prove that the spatial trajectories of the Brownian local time have the same Besov-Orlicz regularity as the Brownian motion itself (i.e. for all t>0, a.s. the function x → L t ( x ) belongs to the Besov-Orlicz space B M 2 , ∞ 1 / 2 with M 2 ( x ) = e | x | 2 - 1 ). Our result is optimal.

Regularity of irregularities on a brownian path

Samuel James Taylor (1974)

Annales de l'institut Fourier

On a standard Brownian motion path there are points where the local behaviour is different from the pattern which occurs at a fixed t 0 with probability 1. This paper is a survey of recent results which quantity the extent of the irregularities and show that the exceptional points themselves occur in an extremely regular manner.

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