White and colored Gaussian noises as limits of sums of random dilations and translations of a single function
Abstract
It is shown that a stochastic process obtained by taking random sums of dilations and translations of a given function converges to Gaussian white noise if a dilation parameter grows to infinity and that it converges to Gaussian colored noise if a scaling parameter for the translations grows to infinity. In particular, the question of when one obtains fractional Brownian motion by integrating this colored noise is studied.
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Pages: 507-516
Publication Date: September 5, 2011
DOI: 10.1214/ECP.v16-1650
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