Electronic Journal of Probability
- Electron. J. Probab.
- Volume 13 (2008), paper no. 39, 1140-1165.
Gaussian Moving Averages and Semimartingales
In the present paper we study moving averages (also known as stochastic convolutions) driven by a Wiener process and with a deterministic kernel. Necessary and sufficient conditions on the kernel are provided for the moving average to be a semimartingale in its natural filtration. Our results are constructive - meaning that they provide a simple method to obtain kernels for which the moving average is a semimartingale or a Wiener process. Several examples are considered. In the last part of the paper we study general Gaussian processes with stationary increments. We provide necessary and sufficient conditions on spectral measure for the process to be a semimartingale.
Electron. J. Probab., Volume 13 (2008), paper no. 39, 1140-1165.
Accepted: 22 July 2008
First available in Project Euclid: 1 June 2016
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Basse, Andreas. Gaussian Moving Averages and Semimartingales. Electron. J. Probab. 13 (2008), paper no. 39, 1140--1165. doi:10.1214/EJP.v13-526. https://projecteuclid.org/euclid.ejp/1464819112