Journal of Applied Probability

Weak approximation for a class of Gaussian processes

Rosario Delgado and Maria Jolis

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 27 February 2002

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Weak convergence Gaussian process Poisson process fractional Brownian motion


Delgado, Rosario; Jolis, Maria. Weak approximation for a class of Gaussian processes. J. Appl. Probab. 37 (2000), no. 2, 400--407. doi:10.1239/jap/1014842545.

Export citation