O-U is continuous time mean reverting process, hence used to model stationary series. It has closed form analytic solution. This allows insight into stationary processes and act like asymptotic limiting case for calculating coefficients that matter. 

I think you want something like this from AR(1) below
$$x_{k+1} = c + a x_k + b\varepsilon_k$$
and substitute c=θμΔt, a=−θΔt and $b = \sigma\sqrt{\Delta t} \space$ 
to get OU 
$$ x_{k+1} = \theta(\mu - x_k)\Delta t + \sigma \varepsilon_k\sqrt{\Delta t}$$