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"Random" Random Matrix Products
"... . The paper deals with compositions of independent random bundle maps whose distributions form a stationary process which leads to study of Markov processes in random environments. A particular case of this situation is a product of independent random matrices with stationarily changing distribution ..."
Abstract

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. The paper deals with compositions of independent random bundle maps whose distributions form a stationary process which leads to study of Markov processes in random environments. A particular case of this situation is a product of independent random matrices with stationarily changing distributions. I obtain results concerning invariant ltrations for such systems, positivity and simplicity of the largest Lyapunov exponent, as well as the central limit theorem type results. An application to random harmonic functions and measures is also considered. Continuous time versions of these results are also discussed which yield applications to linear stochastic dierential equations in random environments. Partially supported by the Edmund Landau Center for Research in Mathematical Analysis and Related Areas, sponsored by the Minerva Foundation (Germany). Typeset by A M ST E X 1 2 Y. KIFER 1. Introduction Starting from the beginning of sixties a lot of work has been done on products o...