Spatial Estimates for Stochastic Flows in Euclidean Space

Authors

Salah-Eldin A. Mohammed, Southern Illinois University CarbondaleFollow
Michael K. R. Scheutzow, Technical University of Berlin

Comments

Published in Annals of Probability, 26(1), 56-77.

Abstract

We study the behavior for large |x| of Kunita-type stochastic flows φ(t, ω, 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.

Recommended Citation

Mohammed, Salah-Eldin A. and Scheutzow, Michael K. "Spatial Estimates for Stochastic Flows in Euclidean Space." (Jan 1998).