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.
Stochastic dynamical systems with weak contractivity properties II. Iteration of Lipschitz mappings
In this continuation of the preceding paper (Part I), we consider a sequence of i.i.d. random Lipschitz mappings → , where is a proper metric space. We investigate existence and uniqueness of invariant measures, as well as recurrence and ergodicity of the induced stochastic dynamical system (SDS) starting at x ∈ . The main results concern the case when the associated Lipschitz constants are log-centered. Principal tools are local contractivity, as considered in detail in Part I, the Chacon-Ornstein...
Stochastic dynamical systems with weak contractivity properties I. Strong and local contractivity
Consider a proper metric space and a sequence of i.i.d. random continuous mappings → . It induces the stochastic dynamical system (SDS) starting at x ∈ . In this and the subsequent paper, we study existence and uniqueness of invariant measures, as well as recurrence and ergodicity of this process. In the present first part, we elaborate, improve and complete the unpublished work of Martin Benda on local contractivity, which merits publicity and provides an important tool for studying stochastic...
Stochastic foundations of the universal dielectric response
We present a probabilistic model of the microscopic scenario of dielectric relaxation. We prove a limit theorem for random sums of a special type that appear in the model. By means of the theorem, we show that the presented approach to relaxation phenomena leads to the well known Havriliak-Negami empirical dielectric response provided the physical quantities in the relaxation scheme have heavy-tailed distributions. The mathematical model, presented here in the context of dielectric relaxation, can...
Stochastic Random Walk Summability.
Strong disorder in semidirected random polymers
We consider a random walk in a random potential, which models a situation of a random polymer and we study the annealed and quenched costs to perform long crossings from a point to a hyperplane. These costs are measured by the so called Lyapounov norms. We identify situations where the point-to-hyperplane annealed and quenched Lyapounov norms are different. We also prove that in these cases the polymer path exhibits localization.
Strong laws of large numbers for sequences of blockwise and pairwise -dependent random variables in metris spaces
The aim of the paper is to establish strong laws of large numbers for sequences of blockwise and pairwise -dependent random variables in a convex combination space with or without compactly uniformly integrable condition. Some of our results are even new in the case of real random variables.
Strong limit theorems for a simple random walk on the 2-dimensional comb.
Subdiffusive behavior of random walk on a random cluster
Subexponential tail asymptotics for a random walk with randomly placed one-way nodes
Sul problema del ritorno all’equilibrio
Si considera, sul gruppo degli interi, una passeggiata aleatoria uscente dall’origine, i cui passi ammettano due soli possibili valori: uno strettamente negativo, l’altro strettamente positivo. Nel caso particolare in cui il primo di questi valori sia , si dà un’espressione esplicita per la legge del primo istante di ritorno nell’origine.