On the strong and weak solutions of stochastic differential equations governing Bessel processes

Abstract

We prove that the δ-dimensional Bessel process (δ > 1) is a strong solution of a stochastic differential equation of the special form. The purpose of this paper is to investigate whether there exist other (weak and strong) solutions of these equations. This leads us to the conclusion that Zvonkin's theorem cannot be extended to stochastic differential equations with an unbounded drift.