Lq-stability of products of block-triangular stationary random matrices
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 ¿^-stability for i.i.d. sequences of blocktriangular random matrices. A known sufficient condition for Lg-stability of an i.i.d. seq...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2008
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| Sorozat: | Acta scientiarum mathematicarum
74 No. 3-4 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16280 |
| Tartalmi kivonat: | 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 ¿^-stability for i.i.d. sequences of blocktriangular random matrices. A known sufficient condition for Lg-stability of an i.i.d. sequence of random matrices An, with q even, is that p[E(j4®9)] < 1, where p 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 Lg-stability, and a simple proof of the above sufficient condition will be given. Two major areas of applications, modelling and estimation of bilinear time series and stochastic volatility processes will be also briefly described. |
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| Terjedelem/Fizikai jellemzők: | 927-944 |
| ISSN: | 0001-6969 |