XV: 43, 627-631, LNM 850 (1981)
WANG, Jia-Gang
Some remarks on processes with independent increments (Independent increments)
This paper contains results on non-homogeneous processes with independent increments, without fixed discontinuities, which belong to the folklore of the subject but are hard to locate in the literature. The first one is that their natural filtration, merely augmented by all sets of measure $0$, is automatically right-continuous and quasi-left-continuous. The second one concerns those processes which are multivariate point processes, i.e., have only finitely many jumps in finite intervals and are constant between jumps. It is shown how to characterize the independent increments property into a property of the process of jumps conditioned by the process of jump times. Finally, a remark is done to the order that several results extend automatically to random measures with independent increments, for which see also 1544
Keywords: Poisson processes, Lévy measures
Nature: Original
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