Electronic Journal of Probability

Gaussian Moving Averages and Semimartingales

Andreas Basse

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Abstract

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.

Article information

Source
Electron. J. Probab., Volume 13 (2008), paper no. 39, 1140-1165.

Dates
Accepted: 22 July 2008
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819112

Digital Object Identifier
doi:10.1214/EJP.v13-526

Mathematical Reviews number (MathSciNet)
MR2424990

Zentralblatt MATH identifier
1191.60043

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60G10: Stationary processes 60G48: Generalizations of martingales 60G57: Random measures

Keywords
semimartingales Gaussian processes stationary processes moving averages stochastic convolutions non-canonical representations

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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


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