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