Hitting probabilities of a Brownian flow with Radial Drift
File(s)
Accepted version
OA Location
Author(s)
Neumann, Eyal
Mueller, Carl
Lee, Jong Jun
Type
Journal Article
Abstract
We consider a stochastic flowφt(x,ω) inRnwith ini-tial pointφ0(x,ω) =x, driven by a singlen-dimensional Brownianmotion, and with an outward radial drift of magnitudeF(‖φt(x)‖)‖φt(x)‖,withFnonnegative, bounded and Lipschitz. We consider initialpointsxlying in a set of positive distance from the origin. Weshow that there exist constantsC∗,c∗>0 not depending onn,such that ifF > C∗nthen the image of the initial set under theflow has probability 0 of hitting the origin. If 0≤F≤c∗n3/4, andif the initial set has nonempty interior, then the image of the sethas positive probability of hitting the origin.
Date Acceptance
2019-04-23
Citation
Annals of Probability, 48 (2), pp.646-671
ISSN
0091-1798
Publisher
Institute of Mathematical Statistics
Start Page
646
End Page
671
Journal / Book Title
Annals of Probability
Volume
48
Issue
2
Copyright Statement
© 2020 copyright The Authors
Subjects
Statistics & Probability
0101 Pure Mathematics
0104 Statistics
Publication Status
Published online
Date Publish Online
2020-03-01