Van Bargen, Holger M. Asymptotic growth of spatial derivatives of isotropic flows. (English) Zbl 1194.60043 Electron. J. Probab. 14, 2328-2351 (2009). 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. Cited in 2 Documents MSC: 60H20 Stochastic integral equations 60G15 Gaussian processes 60G60 Random fields 60F99 Limit theorems in probability theory Keywords:stochastic flows; isotropic Brownian flows; isotropic Ornstein-Uhlenbeck flows; asymptotic behavior of derivatives × Cite Format Result Cite Review PDF Full Text: DOI EuDML EMIS