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2011 White and colored Gaussian noises as limits of sums of random dilations and translations of a single function
Gustaf Gripenberg
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Electron. Commun. Probab. 16: 507-516 (2011). DOI: 10.1214/ECP.v16-1650

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.

Citation

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Gustaf Gripenberg. "White and colored Gaussian noises as limits of sums of random dilations and translations of a single function." Electron. Commun. Probab. 16 507 - 516, 2011. https://doi.org/10.1214/ECP.v16-1650

Information

Accepted: 5 September 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1243.60035
MathSciNet: MR2836757
Digital Object Identifier: 10.1214/ECP.v16-1650

Subjects:
Primary: 60G15
Secondary: 60J65

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