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Asymptotic growth of spatial derivatives of isotropic flows. (English) Zbl 1194.60043
Summary: 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.

##### MSC:
 60H20 Stochastic integral equations 60G15 Gaussian processes 60G60 Random fields 60F99 Limit theorems in probability theory
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