Displaying similar documents to “Sojourn time in ℤ+ for the Bernoulli random walk on ℤ”

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...

Meeting time of independent random walks in random environment

Christophe Gallesco (2013)

ESAIM: Probability and Statistics

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We consider, in the continuous time version, independent random walks on Z in random environment in Sinai’s regime. Let be the first meeting time of one pair of the random walks starting at different positions. We first show that the tail of the quenched distribution of , after a suitable rescaling, converges in probability, to some functional of the Brownian motion. Then we compute the law of this functional. Eventually, we obtain results about the...

A note on quenched moderate deviations for Sinai's random walk in random environment

Francis Comets, Serguei Popov (2010)

ESAIM: Probability and Statistics

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We consider the continuous time, one-dimensional random walk in random environment in Sinai's regime. We show that the probability for the particle to be, at time and in a typical environment, at a distance larger than () from its initial position, is exp{-Const ⋅ ln(1))}.

Large deviations for directed percolation on a thin rectangle

Jean-Paul Ibrahim (2011)

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 [10 (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, 10 (2005) 105–112 (electronic)],...

Smooth and sharp thresholds for random -XOR-CNF satisfiability

Nadia Creignou, Hervé Daudé (2010)

RAIRO - Theoretical Informatics and Applications

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The aim of this paper is to study the threshold behavior for the satisfiability property of a random -XOR-CNF formula or equivalently for the consistency of a random Boolean linear system with variables per equation. For we show the existence of a sharp threshold for the satisfiability of a random -XOR-CNF formula, whereas there are smooth thresholds for and .

Product of exponentials and spectral radius of random k-circulants

Arup Bose, Rajat Subhra Hazra, Koushik Saha (2012)

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

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We consider × random -circulant matrices with → ∞ and = () whose input sequence { }≥0 is independent and identically distributed (i.i.d.) random variables with finite (2 + ) moment. We study the asymptotic distribution of the spectral radius, when = + 1. For this, we first derive the tail behaviour of the fold product of i.i.d. exponential random variables. Then using this tail behaviour result and appropriate normal approximation techniques, we...

Time-homogeneous diffusions with a given marginal at a random time

Alexander M.G. Cox, David Hobson, Jan Obłój (2011)

ESAIM: Probability and Statistics

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We solve explicitly the following problem: for a given probability measure , we specify a generalised martingale diffusion () which, stopped at an independent exponential time , is distributed according to . The process ( ) is specified its speed measure . We present two heuristic arguments and three proofs. First we show how the result can be derived from the solution of [Bertoin and Le Jan, (1992) 538–548.] to the Skorokhod embedding problem....