Limit Theorems for Bessel Processes in General Dimension d

#### A.M. Alhakim, S.A. Molchanov

2012, v.18, №4, 693-700

ABSTRACT

Bessel processes are natural generalizations of the radial part of a Brownian motion in multidimensions. Limit theorems for the first passage time to some neighborhood of the origin play an important role in the spectral theory of Schrodinger type operators. We calculate explicit limit laws in the full range of the parameter $d$ (the "dimension" parameter of the Bessel process) and we establish some kind of symmetry around the singular dimension $d=2$.

Keywords: Bessel process,first entrance time,class $L$ infinitelydivisible law