Abstract
Let μ be an infinitely divisible measure on a finite dimensional vector space. The problem of the existence and the uniqueness of independent martingals for μ is studied. A more detailed description is given for operator semi-stable measures. The results obtained generalize those proved for operator-stable measures by W. N. Hudson, J. D. Mason, and H. G. Tucker 1981, Z. Wahrsch. Verw. Gebiete 58 285–297 and J. A. Veeh 1982, Z. Wahrsch. Verw. Gebiete 61 303–308.
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