"Strong approximations of additive functionals of a planar Brownian
Endre Csáki, Antónia Földes and Yueyun Hu
Summary: This paper is devoted to the study of the additive
functional of a planar Brownian motion. Kasahara and Kotani have
obtained its second-order asymptotic behaviors, by using the
skew-product representation and the ergodicity of the angular part.
We prove that the vector of additive functionals can be strongly
approximated by a multi-dimensional Brownian motion time changed by
an independent inhomogeneous L\'evy process. This strong approximation
yields central limit theorems and almost sure behaviors for additive
functionals. We also give their applications to winding numbers and to
symmetric Cauchy process.
Keywords: Additive functionals; strong approximations.
AMS 2000 subject classification: 60F15; 60J65.