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.
Publié le : 1986-07-14
Classification:
Level crossings,
Cauchy process,
asymptotic distribution,
windings of Brownian motion,
60J30,
60F05,
60G17
@article{1176992437,
author = {Pitman, Jim and Yor, Marc},
title = {Level Crossings of a Cauchy Process},
journal = {Ann. Probab.},
volume = {14},
number = {4},
year = {1986},
pages = { 780-792},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992437}
}
Pitman, Jim; Yor, Marc. Level Crossings of a Cauchy Process. Ann. Probab., Tome 14 (1986) no. 4, pp. 780-792. http://gdmltest.u-ga.fr/item/1176992437/