Displaying similar documents to “Almost-sure growth rate of generalized random Fibonacci sequences”

Disorder relevance for the random walk pinning model in dimension 3

Matthias Birkner, Rongfeng Sun (2011)

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

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We study the continuous time version of the , where conditioned on a continuous time random walk ( )≥0 on ℤ with jump rate > 0, which plays the role of disorder, the law up to time of a second independent random walk ( )0≤≤ with jump rate 1 is Gibbs transformed with weight e (,), where (, ) is the collision local time between and up to time . As the inverse temperature varies, the model undergoes a localization–delocalization...

Sojourn time in ℤ+ for the Bernoulli random walk on ℤ

Aimé Lachal (2012)

ESAIM: Probability and Statistics

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Let (S) be the classical Bernoulli random walk on the integer line with jump parameters  ∈ (01) and  = 1 − . 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 this sojourn time through a particular counting process of the zeros of the walk as done by Chung & Feller [35 (1949) 605–608], simpler representations may be obtained for its probability...

On the volume of intersection of three independent Wiener sausages

M. van den Berg (2010)

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

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Let be a compact, non-polar set in ℝ, ≥3 and let ()={ ()+: 0≤≤, ∈} be Wiener sausages associated to independent brownian motions , =1, 2, 3 starting at 0. The expectation of volume of ⋂=13 () with respect to product measure is obtained in terms of the equilibrium measure of in the limit of large .

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...

A stochastic fixed point equation for weighted minima and maxima

Gerold Alsmeyer, Uwe Rösler (2008)

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

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Given any finite or countable collection of real numbers , ∈, we find all solutions to the stochastic fixed point equation W = d inf j ∈ J T j W j , where and the , ∈, are independent real-valued random variables with distribution and = d means equality in distribution. The bulk of the necessary analysis is spent on the case when ||≥2 and all are (strictly) positive. Nontrivial solutions are then concentrated on either the positive or negative half line. In 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...