Étude asymptotique de certains mouvements browniens complexes avec drift
type: Item
instance of: scholarly article
title: Étude asymptotique de certains mouvements browniens complexes avec drift
zbMATH Open document ID: 0579.60077
DOI: 10.1007/BF00332310
publication date: 1986-01-01T00:00:00Z
review text: We consider a process in the plane solution of the stochastic differential equation: \[ dX_ t=dB_ t+b(X_ t)dt \] where B denotes a two-dimensional Brownian motion and the function \(b:R^ 2\to R^ 2\) satisfies some integrability conditions which ensure that the process X is recurrent. Limit theorems are proved for the winding numbers of B around several points of the plane, which extend \textit{J. W. Pitman} and \textit{M. Yor}'s result in the case without drift [Bull. Am. Math. Soc., New Ser. 10, 109-111 (1984; Zbl 0535.60073) and ''Asymptotic laws of planar Brownian motion.'' Ann. Probab., to appear]. Some limit theorems are also proved for the hitting times of small disks centered at distinct points of the plane, when the radius goes to 0. Similar results hold for Brownian motion with bounded drift on the sphere \(S^ 2\).
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 3928046
zbMATH Keywords: winding numbers
zbMATH Keywords: hitting times of small disks
author: J.-F. Le Gall
author: Marc Yor
MaRDI profile type: Publication
cites work: Q4077321
cites work: Distribution function inequalities for martingales
cites work: On the Decomposition of Continuous Submartingales
cites work: ON CONTINUOUS MARTINGALES
cites work: A new proof of Spitzer's result on the winding of two dimensional Brownian motion
cites work: Asymptotic Behavior of Solutions of Linear Stochastic Differential Systems
cites work: Asymptotic stability and spiraling properties for solutions of stochastic equations
cites work: On skew Brownian motion
cites work: Q3269535
cites work: Q3959169
cites work: Q5332526
cites work: On limit processes for a class of additive functional of recurrent diffusion processes
cites work: Q3344924
cites work: Winding of the plane Brownian motion
cites work: On D. Williams' “Pinching Method” and Some Applications
cites work: The asymptotic joint distribution of windings of planar Brownian motion
cites work: Asymptotic laws of planar Brownian motion
cites work: Q4404207
cites work: Some Theorems Concerning 2-Dimensional Brownian Motion
cites work: Q3862204
cites work: ON STRONG SOLUTIONS OF SOME STOCHASTIC EQUATIONS
cites work: Q3873228
cites work: A TRANSFORMATION OF THE PHASE SPACE OF A DIFFUSION PROCESS THAT REMOVES THE DRIFT
cites work: Q3675284
full work available at URL: https://doi.org/10.1007/bf00332310
OpenAlex ID: W2047969020
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 3928046