Furstenberg's theorem for nonlinear stochastic systems
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Author(s)
Detail(s)
Original language | English |
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Pages (from-to) | 529-534 |
Journal / Publication | Probability Theory and Related Fields |
Volume | 74 |
Issue number | 4 |
Publication status | Published - Apr 1987 |
Externally published | Yes |
Link(s)
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. © 1987 Springer-Verlag.
Citation Format(s)
Furstenberg's theorem for nonlinear stochastic systems. / Carverhill, Andrew.
In: Probability Theory and Related Fields, Vol. 74, No. 4, 04.1987, p. 529-534.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review