Asymptotic Growth of Spatial Derivatives of Isotropic Flows

Holger M van Bargen (Technische Universität Berlin)

Abstract


It is known from the multiplicative ergodic theorem that the norm of the derivative of certain stochastic flows at a previously fixed point grows exponentially fast in time as the flows evolves. We prove that this is also true if one takes the supremum over a bounded set of initial points. We give an explicit bound for the exponential growth rate which is far different from the lower bound coming from the Multiplicative Ergodic Theorem.

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Pages: 2328-2351

Publication Date: October 30, 2009

DOI: 10.1214/EJP.v14-704

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