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Weak approximation for a class of Gaussian processes

Part of: Probability theory on algebraic and topological structures Limit theorems

Published online by Cambridge University Press:  14 July 2016

Rosario Delgado  and
Maria Jolis
Rosario Delgado*
Affiliation:
Universitat Autònoma de Barcelona
Maria Jolis*
Affiliation:
Universitat Autònoma de Barcelona
*
∗Postal address: Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
∗Postal address: Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
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Abstract

We prove that, under rather general conditions, the law of a continuous Gaussian process represented by a stochastic integral of a deterministic kernel, with respect to a standard Wiener process, can be weakly approximated by the law of some processes constructed from a standard Poisson process. An example of a Gaussian process to which this result applies is the fractional Brownian motion with any Hurst parameter.

Keywords

Weak convergenceGaussian processPoisson processfractional Brownian motion

MSC classification

Primary: 60F17: Functional limit theorems; invariance principles 60B10: Convergence of probability measures
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 2 , June 2000 , pp. 400 - 407
Copyright
Copyright © by the Applied Probability Trust 2000 

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Footnotes

Partly supported by grants PB96 0088 and PB96 1182, Dirección General de Enseñanza Superior, and 19955GR593, CIRIT.

References

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