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White and colored Gaussian noises as limits of sums of random dilations and translations of a single function


 
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1. Title Title of document White and colored Gaussian noises as limits of sums of random dilations and translations of a single function
 
2. Creator Author's name, affiliation, country Gustaf Gripenberg; Aalto University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) white noise; colored noise; Brownian motion; fractional Brownian motion; convergence; dilation; translation
 
3. Subject Subject classification 60G15; 60J65
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2011-09-05
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1650
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1650
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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