Abstract
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.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 2, pp. 251–257, February, 1993.
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Koval'chuk, L.V. Semimartingales with values on groups and lie algebras. Ukr Math J 45, 269–276 (1993). https://doi.org/10.1007/BF01060983
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DOI: https://doi.org/10.1007/BF01060983