On weak convergence in dynamical systems to self-similar processes with spectral representation

Author:
Michael T. Lacey

Journal:
Trans. Amer. Math. Soc. **328** (1991), 767-778

MSC:
Primary 60F17; Secondary 28D05, 60F05

DOI:
https://doi.org/10.1090/S0002-9947-1991-1066446-5

MathSciNet review:
1066446

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an aperiodic dynamical system. Set , where is a measurable function on . Let be one of a class of self-similar process with a "nice" spectral representation, for instance, either a fractional Brownian motion, a Hermite process, or a harmonizable fractional stable motion. We show that there is an on , and constants so that

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1991-1066446-5

Keywords:
Aperiodic dynamical system,
weak convergence,
almost sure invariance principle,
spectral representation,
self-similar,
fractional Brownian motion,
Hermite processes,
harmonizable fractional stable motion

Article copyright:
© Copyright 1991
American Mathematical Society