On L2 structure of Markov switching bilinear models

Abdelouahab Bibi; Karima Kimouche

Abdelouahab Bibi University Larbi Ben M'hidi, OEB
Karima Kimouche Department of Mathematics, Larbi Ben M’hidi University , OEB, Algeria and Department of Mathematics, 20 aoˆut 1955 University, Skikda, Algeria

Abstract

In Bibi and Ghazal [2], we have derived several probabilistic properties for time-varying bilinear models where the coefficients vary according to a Markov chain. In this paper, we continue to study certain sufficient conditions in L? for the strict stationarity solution. As a consequence, it can be seen (locally) that when the solution is strictly stationary, it admit also moments of a certain order.