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April, 1987 An Ideal Metric and the Rate of Convergence to a Self-Similar Process
Makoto Maejima, Svetlozar T. Rachev
Ann. Probab. 15(2): 708-727 (April, 1987). DOI: 10.1214/aop/1176992167


A new metric is introduced which is suitable for estimating the rate of convergence of processes related to stable random variables. It is shown that it has an upper bound depending on the difference pseudomoments, but not on the absolute moments. This new metric is then applied to get some rates of convergence to a self-similar process constructed from a stable process.


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Makoto Maejima. Svetlozar T. Rachev. "An Ideal Metric and the Rate of Convergence to a Self-Similar Process." Ann. Probab. 15 (2) 708 - 727, April, 1987.


Published: April, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0624.60010
MathSciNet: MR885139
Digital Object Identifier: 10.1214/aop/1176992167

Primary: 60E05
Secondary: 60E07 , 60F05 , 60G50

Keywords: difference pseudomoment , Fractional calculus , fractional stable process , ideal metric , Method of probability metrics , rate of convergence , self-similar process , stable random variable

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 2 • April, 1987
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