Encyclopedia > Gauss-Markov process

  Article Content

Gauss-Markov process

This article is not about the Gauss-Markov theorem of mathematical statistics.

As one would expect, Gauss-Markov stochastic processes are stochastic processes that satisfy the requirements for both Gaussian processes[?] and Markov processes.

Every Gauss-Markov process X(t) possesses the three following properties:

  • If h(t) is a non-zero scalar function of t, then Z(t) = h(t)X(t) is also a Gauss-Markov process
  • If f(t) is a non-decreasing scalar function of t, then Z(t) = X(f(t)) is also a Gauss-Markov process
  • There exists a non-zero scalar function h(t) and a non-decreasing scalar function f(t) such that X(t) = h(t)W(f(t)), where W(t) is the Standard Wiener Process.

Property (3) means that every Gauss-Markov process can be synthesized from the Standard Wiener Process (SWP).

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article
Kuru Kuru Kururin

...   Contents Kuru Kuru Kururin Kuru Kuru Kururin is a game for the Game Boy Advance. The player controls a slowly spinning stick and must get it through a series of ...

This page was created in 24.5 ms