Abstract

We show that for the products of iid random matrices or for linear It6 equations with constant coefficients the number of the p-th moment Lyapunov exponents g(p, .) with p near zero is not less than the number of the sample Lyapunov exponents ?.[.I and the p-th moment Lyapunov filtration is finer than the sample Lyapunov filtration of Furstenberg and Kifer [FK]. Moreover, the function g(p, x,) is differentiable with respect to p at p = 0 for every 0 + x, E Rd and if i[x,] = ii then This is an extension of the formulae of Molchanov [MI and Arnold [A] to our general situation.