Tail behaviour of stationary solutions of random difference equations: the case of regular matrices

@article{Alsmeyer2012TailBO,
title={Tail behaviour of stationary solutions of random difference equations: the case of regular matrices},
author={Gerold Alsmeyer and Sebastian Mentemeier},
journal={Journal of Difference Equations and Applications},
year={2012},
volume={18},
pages={1305 - 1332}
}
• Published 9 September 2010
• Mathematics
• Journal of Difference Equations and Applications
Given a sequence of i.i.d. random variables with generic copy such that M is a regular matrix and Q takes values in , we consider the random difference equation Under suitable assumptions stated below, this equation has a unique stationary solution R such that for some and some finite positive and continuous function K on , holds true. A rather long proof of this result, originally stated by Kesten [Acta Math. 131 (1973), pp. 207–248] at the end of his famous article, was given by Le Page [S…
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