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January, 1987 Tightness of Products of Random Matrices and Stability of Linear Stochastic Systems
Philippe Bougerol
Ann. Probab. 15(1): 40-74 (January, 1987). DOI: 10.1214/aop/1176992256

Abstract

Let $\mu^n$ be the distribution of a product of $n$ independent identically distributed random matrices. We study tightness and convergence of the sequence $\{\mu^n, n \geq 1\}$. We apply this to linear stochastic differential (and difference) equations, characterize the stability in probability, in the sense of Hashminski, of the zero solution, and find all their stationary solutions.

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Philippe Bougerol. "Tightness of Products of Random Matrices and Stability of Linear Stochastic Systems." Ann. Probab. 15 (1) 40 - 74, January, 1987. https://doi.org/10.1214/aop/1176992256

Information

Published: January, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0614.60008
MathSciNet: MR877590
Digital Object Identifier: 10.1214/aop/1176992256

Subjects:
Primary: 60B15
Secondary: 60B10 , 60H10 , 60H25

Keywords: Convergence in distribution , linear stochastic differential equations , linear stochastic systems , Products of random matrices , stability in probability , stationary solution

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 1 • January, 1987
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