Girsanov showed that under an absolutely continuous change in probability measure a Wiener process is transformed into the sum of a Wiener process and a second process with sample functions which are absolutely continuous. This result has a natural generalization in the context of local martingales. This generalization is derived in this paper, and some of its ramifications are examined. As a simple application, the likelihood ratio for a single-server queueing process with very general arrival and service characteristics is derived.
"Transformation of Local Martingales Under a Change of Law." Ann. Probab. 2 (5) 879 - 888, October, 1974. https://doi.org/10.1214/aop/1176996554