Date Added: May 2011
In this paper, the authors re-examine the analysis of the paper "On the martingale property of stochastic exponentials" by B. Wong and C.C. Heyde [WH04]. Some counterexamples are presented and alternative formulations are discussed. In [WH04], the authors announce very general results about the martingale property of exponential local martingales. Since the subject matter of the paper is important, it is necessary to examine it critically. In Section 2 they describe the setting of [WH04]. In Section 3 they re-examine the analysis in [WH04] and discuss an alternative formulation of their Corollary 2. Section 4 contains counterexamples.