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Integral-geometric construction of self-similar stable processes

Published online by Cambridge University Press:  22 January 2016

Shigeo Takenaka
Shigeo Takenaka*
Affiliation:
Department of Mathematics, Hiroshima University, Kagamiyama 1, Higashi-Hiroshima 742, Japan
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Recently, fractional Brownian motions are widely used to describe complex phenomena in several fields of natural science. In the terminology of probability theory the fractional Brownian motion is a Gaussian process {X(t) : t є R} with stationary increments which has a self-similar property, that is, there exists a constant H (for the Brownian motion H = 1/2, in general 0 < H < 1 for Gaussian processes) called the exponent of self-similarity of the process, such that, for any c > 0, two processes are subject to the same law (see [10]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 123 , September 1991 , pp. 1 - 12
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

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