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On the Multiplicity of a Stochastic Vector Process

Published online by Cambridge University Press:  05 September 2017

Harald Cramér
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Abstract

This note deals with a q-dimensional stochastic vector process x(t) = {x1 (t), …, xq (t)}, satisfying certain stated general conditions. For such a process, there is a representation (1) in terms of stochastic innovations acting throughout the past of the process. The number N of terms in this representation is called the multiplicity of the x(t) process, and is uniquely determined by the process. For a one-dimensional process (q = 1) it is known that under certain conditions we have N = 1. For an arbitrary value of q, this note gives conditions under which we have N ≦ q.

Type
Part V — Stochastic Processes
Information
Journal of Applied Probability , Volume 12 , Issue S1 , 1975 , pp. 187 - 194
Copyright
Copyright © 1975 Applied Probability Trust 

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References

[1] Ephremides, A. and Thomas, J. B. (Editors) (1973) Random Processes, Multiplicity Theory and Canonical Decompositions. Dawden, Hutchinson and Ross. Distributed by Wiley, London.Google Scholar