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On Multivariate Wide-sense Markov Processes*

Published online by Cambridge University Press:  22 January 2016

V. Mandrekar
V. Mandrekar*
Affiliation:
University of Minnesota
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The idea of multivariate wide-sense Markov processes has been recently used by F.J. Beutler [1], In his paper, he shows that the solution of a linear vector stochastic differential equation in a wide-sense Markov process. We obtain here a characterization of such processes and as its consequence obtain the conditions under which it satisfies Beutler’s equation. Furthermore, in stationary Gaussian case we show that these are precisely stationary Gaussian Markov processes studied by J. Doob [5].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 33 , November 1968 , pp. 7 - 19
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

Footnotes

*)

This research was supported by U.S. Army Research Office, Grant No. DA-ARO-D-31-124-G562 and U.S. Air Force Office of Scientific Research, Grant No. AFOSR-381-65. Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No.: DA-31-124-ARO-D-462.

References

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