@article{5473ab52ced54b1e8528dfbdab6f7487, title = "Furstenberg's theorem for nonlinear stochastic systems", abstract = "We extend Furstenberg's theorem to the case of an i.i.d. random composition of incompressible diffeomorphisms of a compact manifold M. The original theorem applies to linear maps {Xi}i∈N on ℝm with determinant 1, and says that the highest Lyapunov exponent {Mathematical expression} is strictly positive unless there is a probability measure on the projective (m-1)-space which is a.s. invariant under the action of Xi. Our extension refers to a probability measure on the projective bundle over M. We show that when our diffeomorphism is the flow of a stochastic differential equation, the criterion for β>0 is ensured by a Lie algebra condition on the induced system on the principal bundle over M. {\textcopyright} 1987 Springer-Verlag.", author = "Andrew Carverhill", year = "1987", month = apr, doi = "10.1007/BF00363514", language = "English", volume = "74", pages = "529--534", journal = "Probability Theory and Related Fields", issn = "0178-8051", publisher = "Springer", number = "4", }