Gauss–Markov process

As one would expect, Gauss-Markov stochastic processes satisfy the requirements for both Gaussian processes and Markov Processes. Gauss-Markov processes possess the three following properties:

Given that X(t) is a Gauss-Markov process:

(1) Z(t) = h(t)X(t) is also a Gauss-Markov process

   where h(t) is a scalar function of t.

(2) Z(t) = X(f(t)) is also a Gauss-Markov process

   where f(t) is a non-decreasing scalar function of t.

(3) X(t) = h(t)W(f(t))

   where W(t) is the Standard Wiener Process and h(t) and f(t) obey the above criteria.

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