The Annals of Probability
- Ann. Probab.
- Volume 26, Number 1 (1998), 56-77.
Spatial estimates for stochastic flows in Euclidean space
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.
Ann. Probab., Volume 26, Number 1 (1998), 56-77.
First available in Project Euclid: 31 May 2002
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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