Abstract
The characteristic function, cumulants and moments of vector-valued multidimensional processes, satisfying properties similar to stationary independent increments, are derived. By considering a set of additional postulates for such processes, it is shown that the marginal distribution of such processes is multivariate Poisson. Some of the results in this paper are extensions of the properties of the first two moments of a univariate one-dimensional process with stationary independent increments.
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Paul, V., Chandrasekar, B. Some results for multidimensional stationary independent increment processes. Statistical Papers 34, 59–65 (1993). https://doi.org/10.1007/BF02925527
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DOI: https://doi.org/10.1007/BF02925527