Department of Mathematics, Louisiana State University, Baton Rouge, LA70803, USA. E-mail: sklin_04@math.lsu.edu
It is well-known that the proof of the Girsanov Theorem involves the local martingale theory. Our motivation for the main result in this paper is the desire to avoid using the local martingale theory in the proof of the Girsanov Theorem, namely we will use only the martingale theory to obtain our result. Many sufficient conditions for the validity of the Girsanov Theorem have been found since the publication of the result by Girsanov in 1960. We will compare our conditions with some of these sufficient conditions.
Girsanov theorem, martingale, local martingale, exponential processes, Schwarz's inequality
