Comparaison des exposants de Lyapounov des processus markoviens multiplicatifs. (Comparison of Lyapunov exponents of multiplicative Markov processes)
The author deals with conditions ensuring that the Lyapunov exponents of a cocycle of random matrices over a Markov chain are distinct. He treats linear Ito equations with Markovian coefficients and cocycles of diffeomorphisms derived from nonlinear stochastic differential equations as particular cases. He proves that the Lyapunov spectrum of the gradient Brownian motion on a compact hypersurface V in \({\mathbb{R}}^{d+1}\) is simple except V is a sphere (of radius r) in which case all exponents are equal to \(-d/2r^ 2\).
scientific article; zbMATH DE number 4100291