In this chapter, we will obtain Girsanov Theorem and its generalizations by Meyer. Let M be a martingale on and let be another probability measure on absolutely continuous w.r.t. Then as noted in Remark 4.26, M is a semimartingale on We will obtain a decomposition of M into N and B, where N is a martingale. This result for Brownian motion was due to Girsanov, and we will also present the generalizations due to Meyer.
Karandikar, R. L., & Rao, B. V. (2018). Girsanov Theorem. In Indian Statistical Institute Series (pp. 411–434). Springer Science and Business Media B.V. https://doi.org/10.1007/978-981-10-8318-1_13