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Weak approximation for a class of Gaussian processes

Published online by Cambridge University Press:  14 July 2016

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

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.

Type
Research Papers
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

Billingsley, P. (1968). Convergence of Probability measures. John Wiley. New York.Google Scholar
Decreusefond, L. and Üstünel, A. S. (1999). Stochastic analysis of the fractional Brownian motion. Potential Analysis 10, 177214.Google Scholar
Hida, T., and Hitsuda, M. (1976). Gaussian Processes (Translations of Mathematical Monographs 120). American Mathematical Society, Providence, RI.Google Scholar
Mandelbrot, B. B., and Van Ness, J. W. (1968). Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10, 422437.CrossRefGoogle Scholar
Stroock, D. W. (1982). Topics in Stochastic Differential Equations. Tata Institute of Fundamental Research & Springer, Berlin.Google Scholar