Scaling Limit, Noise, Stability

Details Scaling Limit, Noise, Stability Scaling Limit, Noise, Stability

2003-01-21

arxiv.org/abs/math/0301237v1

Lect. Notes Math. 1840 (2004), 1-106.

Mathematics

Probability

A summer school course, 108 pages, 42 small figs

Scientific paper

Linear functions of many independent random variables lead to classical noises (white, Poisson, and their combinations) in the scaling limit. Some singular stochastic flows and some models of oriented percolation involve very nonlinear functions and lead to nonclassical noises. Two examples are examined, Warren's `noise made by a Poisson snake' and the author's `Brownian web as a black noise'. Classical noises are stable, nonclassical are not. A new framework for the scaling limit is proposed. Old and new results are presented about noises, stability, and spectral measures.

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