Open Access
July, 1986 Level Crossings of a Cauchy Process
Jim Pitman, Marc Yor
Ann. Probab. 14(3): 780-792 (July, 1986). DOI: 10.1214/aop/1176992437


The asymptotic distribution as $t \rightarrow \infty$ is obtained for the number of jumps of a symmetric Cauchy process across level $x$ up to time $t$, jointly as $x$ varies. This result is related to the asymptotic joint distribution of windings of a planar Brownian motion about several points.


Download Citation

Jim Pitman. Marc Yor. "Level Crossings of a Cauchy Process." Ann. Probab. 14 (3) 780 - 792, July, 1986.


Published: July, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0602.60059
MathSciNet: MR841583
Digital Object Identifier: 10.1214/aop/1176992437

Primary: 60J30
Secondary: 60F05 , 60G17

Keywords: asymptotic distribution , Cauchy process , level crossings , windings of Brownian motion

Rights: Copyright © 1986 Institute of Mathematical Statistics

Vol.14 • No. 3 • July, 1986
Back to Top