Open Access
January 1998 Spatial estimates for stochastic flows in Euclidean space
Salah-Eldin A. Mohammed, Michael K. R. Scheutzow
Ann. Probab. 26(1): 56-77 (January 1998). DOI: 10.1214/aop/1022855411


We study the behavior for large $|x|$ of Kunita-type stochastic flows $\phi(t, \omega x)$ on $R^d$, driven by continuous spatial semimartingales. For this class of flows we prove new spatial estimates for large $|x|$, under very mild regularity conditions on the driving semimartingale random field. It is expected that the results would be of interest for the theory of stochastic flows on noncompact manifolds as well as in the study of nonlinear filtering, stochastic functional and partial differential equations. Some examples and counterexamples are given.


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Salah-Eldin A. Mohammed. Michael K. R. Scheutzow. "Spatial estimates for stochastic flows in Euclidean space." Ann. Probab. 26 (1) 56 - 77, January 1998.


Published: January 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0937.60056
MathSciNet: MR1617041
Digital Object Identifier: 10.1214/aop/1022855411

Primary: 60H10 , 60H20
Secondary: 60H25

Keywords: local characteristics , Quadratic Variation , spacial semimartingale , stochastic differential equation (s.d.e.) , stochastic flow

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 1 • January 1998
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