The Annals of Probability

Spatial estimates for stochastic flows in Euclidean space

Salah-Eldin A. Mohammed and Michael K. R. Scheutzow

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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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Ann. Probab., Volume 26, Number 1 (1998), 56-77.

First available in Project Euclid: 31 May 2002

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Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H20: Stochastic integral equations
Secondary: 60H25: Random operators and equations [See also 47B80]

Stochastic flow spacial semimartingale local characteristics quadratic variation stochastic differential equation (s.d.e.)


Mohammed, Salah-Eldin A.; Scheutzow, Michael K. R. Spatial estimates for stochastic flows in Euclidean space. Ann. Probab. 26 (1998), no. 1, 56--77. doi:10.1214/aop/1022855411.

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