## Annals of Probability

### Spatial estimates for stochastic flows in Euclidean space

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 31 May 2002

https://projecteuclid.org/euclid.aop/1022855411

Digital Object Identifier
doi:10.1214/aop/1022855411

Mathematical Reviews number (MathSciNet)
MR1617041

Zentralblatt MATH identifier
0937.60056

#### Citation

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. https://projecteuclid.org/euclid.aop/1022855411

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• CARBONDALE, ILLINOIS 62901 STRASSE DES 17 JUNI 136 E-MAIL: salah@math.siu.edu D-10623 BERLIN WEB PAGE: http: salah.math.siu.edu GERMANY E-MAIL: ms@math.tu-berlin.de