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.