Lq-stability of products of block-triangular stationary random matrices

Gerencsér, László and Orlovits, Zsanett (2008) Lq-stability of products of block-triangular stationary random matrices. Acta Scientiarum Mathematicarum, 74. pp. 927-944.

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Abstract

The purpose of this paper is to extend a recent result on the Lyapunov-exponent of a stationary, ergodic sequence of block-triangular random matrices to the problem of L_q-stability for i.i.d. sequences of block-triangular random matrices. A known sufficient condition for L_q-stability of an i.i.d. sequence of random matrices A_n, with q even, is that rho [ E(A^{otimes q})] <1, where rho is the spectral radius. It is shown that the validity of this condition for the diagonal blocks of A implies its validity for the full matrix, see Theorem 1.1. A brief survey of results on L_q-stability, and a simple proof of the above sufficient condition will be given. Two major area of applications, modelling and estimation of bilinear time series and stochastic volatility processes will be also briefly described.

Item Type: Article
Uncontrolled Keywords: Random matrix products; Lyapunov exponents; GARCH processes
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Depositing User: Eszter Nagy
Date Deposited: 11 Dec 2012 15:31
Last Modified: 11 Dec 2012 15:31
URI: http://eprints.sztaki.hu/id/eprint/5427

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