## Journal of Applied Probability

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

### Weak approximation for a class of Gaussian processes

Rosario Delgado and Maria Jolis

#### 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 in Project Euclid: 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. J. Appl. Probab. 37 (2000), no. 2, 400--407. doi:10.1239/jap/1014842545. http://projecteuclid.org/euclid.jap/1014842545.