Displaying similar documents to “Fractional multiplicative processes”

An integral test for the transience of a brownian path with limited local time

Itai Benjamini, Nathanaël Berestycki (2011)

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

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We study a one-dimensional brownian motion conditioned on a self-repelling behaviour. Given a nondecreasing positive function (), ≥0, consider the measures obtained by conditioning a brownian path so that ≤(), for all ≤, where is the local time spent at the origin by time . It is shown that the measures are tight, and that any weak limit of as →∞ is transient provided that −3/2() is integrable. We conjecture...

Branching brownian motion with an inhomogeneous breeding potential

J. W. Harris, S. C. Harris (2009)

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

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This article concerns branching brownian motion (BBM) with dyadic branching at rate || for a particle with spatial position ∈ℝ, where >0. It is known that for >2 the number of particles blows up almost surely in finite time, while for =2 the expected number of particles alive blows up in finite time, although the number of particles alive remains finite almost surely, for all time. We define the right-most particle, , to be the supremum of the spatial positions...

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

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In this paper we study a random walk on an affine building of type , 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 ( (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...

Strong law of large numbers for branching diffusions

János Engländer, Simon C. Harris, Andreas E. Kyprianou (2010)

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

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Let be the branching particle diffusion corresponding to the operator +(2−) on ⊆ℝ (where ≥0 and ≢0). Let denote the generalized principal eigenvalue for the operator + on and assume that it is finite. When >0 and +− satisfies certain spectral theoretical conditions, we prove that the random measure {− } converges almost surely in the vague topology as tends to infinity. This result...

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]...