Could you, please, help me figure out the following problem. 

We call a stationary Gaussian process $\xi\_t$ (with continuous paths) an Ornstein-Uhlenbeck process if its correlation function $\mathbb{E}\xi\_{s+t}\bar \xi\_s$ is
$$
\mathbb{E}\xi\_{s+t}\bar \xi\_s=R(t)=R(0)e^{-\alpha|t|}, \alpha\ge 0
$$

The question is that Ornstein-Uhlenbeck process is the unique Markovian stationary Gaussian process. 

By Markovian I mean that
$$
\mathbb{E}\left(f(\xi\_t|\xi\_{t\_n},\ldots, \xi\_{t\_1}\right)=\mathbb{E}\left(f(\xi\_t|\xi\_{t\_n}\right).
$$
for $t\_1\le t\_2\le\ldots\le t\_n\le t$ and any Borel-measurable funciton $f$.

This problem amazed me at first glance. 

I can't figure out how to deduce 'exponential decay' of correlation function $R(t)$ from Markovian property.