Gaussian Markov processes

Show that it corresponds to following kernels:

• Ornstein-Uhlenbeck kernel
• Wiener kernel

Link to $AR(n)$ processes and stochastic differential equations.

Exponential autocorrelation:

\begin{equation}
 \mathbf{R} (\tau) = \sigma^{2}\, \exp \left( - \beta |\tau| \right)
\end{equation}