I have the following stochastic sequence $t_n$ with the following recurrent equation:
$$t_n = \max(t_{n-1} - \tau, 0) + a_n,$$
where $\tau$ is known constant, $a_n$ are independent and identically distributed random variables with mean $\mu_0$ and variance $\sigma_0^2$.
I would like to know stationary conditions for this process. Any references are also welcome since I don't know how this process is properly called in the literature.