Consider a discreet time series / stochastic process -

$\displaystyle x_t = \rho x_{t-1} + \epsilon_t$

where $\displaystyle \epsilon_t$ is white noise i.e. iid ~$\displaystyle N(0,\sigma^2)$

I need to to prove this series is weak stationary when $\displaystyle |\rho| < 1 $

Definition of weak stationary, I have/use
1. $\displaystyle E(x_t)$ = constant, $\displaystyle \mu$ (independent of t)
2. $\displaystyle E(x_t.x_{t+k}) = f(k)$ i.e. independent of t, it is just a function of lag period, k.

I know this is a pretty basic question, but not really able to go ahead here. Can anyone please help with pointers, references, outline of the proof. Thanks