Title: Conditions for the existence of stationary and causal space-time bilinear model and central limit theorem

Authors: Soumia Kharfouchi; Houda Mehri

Addresses: Department of Mathematics, Mentouri University, Constantine, Algeria ' Research Unit in Applied Mathematics & Mathematical Physics "AMMP" Preparatory Institute to the Military Academies Avenue Maréchal Tito 4029 Sousse, Tunisia

Abstract: In this paper, we present a spatio-temporal model that provides a spatial structure to bilinear processes. The organisation of the paper is as follows: in Section 2, we introduce some definitions and recall some results about space-time bilinear models. In Section 3, we establish, under the minimal set of assumptions, the existence and time stationarity of Xt(u). Our main result is given the Section 4, where a Central Limit Theorem (CLT) is obtained. In Section 5, we give some simple examples.

Keywords: spatio-temporal models; stationarity; asymptotic normality; bilinear process; central limit theorem; CLT; modelling.

DOI: 10.1504/IJMOR.2012.049937

International Journal of Mathematics in Operational Research, 2012 Vol.4 No.6, pp.638 - 650

Available online: 19 Oct 2012 *

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