Gauss–Markov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes. A stationary Gauss–Markov process is unique^{[citation needed]} up to rescaling; such a process is also known as an Ornstein–Uhlenbeck process.

Gauss–Markov processes obey Langevin equations.

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

Property (3) means that every non-degenerate mean-square continuous 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.

There are also some trivial exceptions to all of the above.^{[clarification needed]}