# Is Ornstein–Uhlenbeck process the continuous-time correspondence of AR(1) process?

I see the AR(1) process (with $$|\alpha| < 1$$) can be written in the following way: $$x_{t+1} = \alpha x_t + \epsilon_t$$ $$\Delta x_t = - (1 - \alpha) x_t + \epsilon_t$$ which looks quite like the formula of Ornstein–Uhlenbeck process without a drift term as $$dx_t = -\theta x_t + \sigma dW_t$$ then is OU process the continuous-time correspondence of AR(1) process?

Ignore the question below if it is not. If I have the value of parameters of AR(1) process, i.e. $$\alpha$$, variance of $$\epsilon$$, and time difference $$\Delta_t$$, how do I convert these parameters to the parameter of OU process?