Semimartingales with values on groups and Lie algebras - Kovalchuk, L. V. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
We establish a one-to-one correspondence between the processes taking values on the Lie group and its Lie algebra. This correspondence preserves the main properties of the processes: semimartingale property with respect to a certain flow, independence of increments, and continuity.