Gauss–Markov process

Gauss–Markov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are that satisfy the requirements for both Gaussian processes and Markov processes. The stationary Gauss–Markov process (also known as a Ornstein–Uhlenbeck process) is a very special case because it is unique, except for some trivial exceptions.

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

Property (3) means that every Gauss–Markov process can be synthesized from the standard Wiener process (SWP).

A stationary Gauss–Markov process with variance ${\displaystyle {\textbf {E}}(X^{2}(t))=\sigma ^{2}}$ and time constant ${\displaystyle \beta ^{-1}}$ has the following properties.

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