Small-time behaviour of Lévy processes.
Soft local times and decoupling of random interlacements
In this paper we establish a decoupling feature of the random interlacement process at level , . Roughly speaking, we show that observations of restricted to two disjoint subsets and of are approximately independent, once we add a sprinkling to the process by slightly increasing the parameter . Our results differ from previous ones in that we allow the mutual distance between the sets and to be much smaller than their diameters. We then provide an important application of this...
Sojourn time in ℤ+ for the Bernoulli random walk on ℤ
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 this sojourn time through a particular counting process of the zeros of the walk as done by Chung & Feller [Proc. Nat. Acad. Sci. USA 35 (1949) 605–608], simpler representations may be obtained...
Sojourn time in ℤ+ for the Bernoulli random walk on ℤ
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 this sojourn time through a particular counting process of the zeros of the walk as done by Chung & Feller [Proc. Nat. Acad. Sci....
Sojourn times.
Sojourn times for the Brownian motion.
Some LIL type results on the partial sums and trimmed sums with multidimensional indices.
Some recent results on the law of the iterated logarithm for Banach space valued random variables
Some remarks on the random walk on finite groups
Some results on summability of random variables.
Some use of some “symmetries” of some random process
Spectral type of a polynomial of stationary Gaussian process
Spitzer's condition for random walks and Lévy processes
Stabilité du comportement des marches aléatoires sur un groupe localement compact
Dans cet article nous démontrons un théorème de stabilité des probabilités de retour sur un groupe localement compact unimodulaire, séparable et compactement engendré. Nous démontrons que le comportement asymptotique de F*(2n)(e) ne dépend pas de la densité F sous des hypothèses naturelles. A titre d’exemple nous établissons que la probabilité de retour sur une large classe de groupes résolubles se comporte comme exp(−n1/3).
Stability and other limit laws for exit times of random walks from a strip or a halfplane
Stability estimates of generalized geometric sums and their applications
The upper bounds of the uniform distance between two sums of a random number of independent random variables are given. The application of these bounds is illustrated by stability (continuity) estimating in models in queueing and risk theory.
Stationary measures for random walks in a random environment with random scenery.
Stationary random graphs on with prescribed iid degrees and finite mean connections.
Stationary random graphs with prescribed iid degrees on a spatial Poisson process.
Stochastic analysis of Bernoulli processes.