Level crossings of a Cauchy process
The authors use the well-known skew-product representation of planar Brownian motion, and a simple argument involving Brownian scaling and renewal theory for an embedded random walk, to establish the asymptotic behaviour of numbers of large, small, and medium crossings of zero by a Cauchy process. They further apply the results of a comparison paper to establish results for different kinds of crossings at two different levels.
skew-product representation of planar Brownian motion
scientific article; zbMATH DE number 3971910