Journal of Applied Probability

Weak approximation for a class of Gaussian processes

Rosario Delgado and Maria Jolis

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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.

Article information

Source
J. Appl. Probab. Volume 37, Number 2 (2000), 400-407.

Dates
First available: 27 February 2002

Permanent link to this document
http://projecteuclid.org/euclid.jap/1014842545

Digital Object Identifier
doi:10.1239/jap/1014842545

Mathematical Reviews number (MathSciNet)
MR1780999

Zentralblatt MATH identifier
0968.60008

Subjects
Primary: 60FXX 60F17: Functional limit theorems; invariance principles 60B10: Convergence of probability measures

Keywords
Weak convergence Gaussian process Poisson process fractional Brownian motion

Citation

Delgado, Rosario; Jolis, Maria. Weak approximation for a class of Gaussian processes. Journal of Applied Probability 37 (2000), no. 2, 400--407. doi:10.1239/jap/1014842545. http://projecteuclid.org/euclid.jap/1014842545.


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