Abstract
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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© 2004 Springer-Verlag Berlin/Heidelberg
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Tsirelson, B. (2004). Boris Tsirelson: Scaling Limit, Noise, Stability. In: Picard, J. (eds) Lectures on Probability Theory and Statistics. Lecture Notes in Mathematics, vol 1840. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39982-7_1
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DOI: https://doi.org/10.1007/978-3-540-39982-7_1
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Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-540-39982-7
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