Nguyen Huu Du and Phan Le Na

Abstract

        The article concerned with the problem of regarding Lyapunov exponents of a random difference equation as the spectrum of an operator acting on a suitable space. Let L be the set of all sequences of random variables having finite p^th moments for some p small, endowed with a certain topology. From the difference equation X(n+1) = A(n) X(n) ; X(0)=x Î R^d, where (A(n), n Î Z) is an i.i.d. sequence of random variables, we construct an operator T acting on the space L. It is proved that the spectrum of the operator T is contained in the set of sample Lyapunov exponents of this random dynamical system.