The General Stationary Gaussian Markov Process

Larry Brown; Philip Ernst; Larry Shepp; Bob Wolpert

The General Stationary Gaussian Markov Process

Probability 2014-01-03 v1

Authors: Larry Brown , Philip Ernst , Larry Shepp , Bob Wolpert

Abstract

We find the class, ${\cal{C}}_k, k \ge 0$ , of all zero mean stationary Gaussian processes, $Y(t), ~t \in \reals$ with $k$ derivatives, for which \begin{equation} Z(t) \equiv (Y^{(0)}(t), Y^{(1)}(t), \ldots, Y^{(k)}(t) ), ~ t \ge 0 \end{equation} \noindent is a $(k+1)$ -vector Markov process. (here, $Y^{(0)}(t) = Y(t)$ ).

Keywords

markov processes

Cite

@article{arxiv.1401.0251,
  title  = {The General Stationary Gaussian Markov Process},
  author = {Larry Brown and Philip Ernst and Larry Shepp and Bob Wolpert},
  journal= {arXiv preprint arXiv:1401.0251},
  year   = {2014}
}

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13 pages, 0 figures

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