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Spatial estimates for stochastic flows in Euclidean space. (English) Zbl 0937.60056

Summary: We study the behavior for large \(|x|\) of Kunita-type stochastic flows \(\varphi(t,\omega,x)\) 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.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations
60H25 Random operators and equations (aspects of stochastic analysis)
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[17] 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 URL:
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