Scaling limits for symmetric Itô–Lévy processes in random medium

Scaling limits for symmetric Itô-Lévy processes in random medium

Abstract We are concerned with scaling limits of the solutions to stochastic differential equations with stationary coefficients driven by Poisson random measures and Brownian motions. We state an annealed convergence theorem, in which the limit exhibits a diffusive or superdiffusive behavior, depending on the integrability properties of the Poisson random measure.

Scaling Limits for Cumulative Input Processes

We study different scaling behavior of very general telecommunications cumulative input processes. The activities of a telecommunication system are described by a marked-point process Tn Zn n∈ , where Tn is the arrival time of a packet brought to the system or the starting time of the activity of an individual source, and the mark Zn is the amount of work brought to the system at time Tn. This ...

Random fractals and scaling limits in percolation

Kinetic limits for waves in a random medium

2 Diffusive limit for a particle in a random flow 7 2.1 Diffusion of a particle in a time-dependent random flow . . . . . . . . . . . . . . . . 7 2.1.1 The central limit theorem, purely time-dependent flows, and diffusion . . . . 8 2.1.2 Using formal asymptotic expansions . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 Random flows with spatial-temporal dependence . . . . . . . . . . . . ...

Scaling limits of large random trees

The goal of these lectures is to survey some of the recent progress on the description of largescale structure of random trees. We will use the framework of Markov branching sequences of trees and develop several applications, to combinatorial trees, Galton-Watson trees, some dynamical models of randomly growing trees, cut trees, etc. This is a rough draft – to be completed – all comments are w...