Open Access
2009 Asymptotic Growth of Spatial Derivatives of Isotropic Flows
Holger van Bargen
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Electron. J. Probab. 14: 2328-2351 (2009). DOI: 10.1214/EJP.v14-704


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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Holger van Bargen. "Asymptotic Growth of Spatial Derivatives of Isotropic Flows." Electron. J. Probab. 14 2328 - 2351, 2009.


Accepted: 30 October 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1194.60043
MathSciNet: MR2556020
Digital Object Identifier: 10.1214/EJP.v14-704

Primary: 60G15
Secondary: 60F99 , 60G60

Keywords: asymptotic behavior of derivatives , isotropic Brownian flows , isotropic Ornstein-Uhlenbeck flows , Stochastic flows

Vol.14 • 2009
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