On Multivariate Wide-sense Markov Processes
- 1 November 1968
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 33, 7-19
- https://doi.org/10.1017/s0027763000012824
Abstract
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].Keywords
This publication has 6 references indexed in Scilit:
- The square-integrability of matrix-valued functions with respect to a non-negative Hermitian measureDuke Mathematical Journal, 1964
- Multivariate Wide-sense Markov Processes and Prediction TheoryThe Annals of Mathematical Statistics, 1963
- On the structure of purely non-deterministic stochastic processesArkiv för Matematik, 1961
- Canonical representations of Gaussian processes and their applicationsKyoto Journal of Mathematics, 1960
- The prediction theory of multivariate stochastic processes: I. The regularity conditionActa Mathematica, 1957
- The Elementary Gaussian ProcessesThe Annals of Mathematical Statistics, 1944