Distribution of first-return times in correlated stationary signals

We present an analytical expression for the first return time (FRT) probability density function of a stationary correlated signal. Precisely, we start by considering a stationary discrete-time Ornstein-Uhlenbeck (OU) process with exponenial decaying correlation function. The first return time distribution for this process is derived by adopting a well known formalism typically used in the study of the FRT statistics for non-stationary diffusive processes. Then, by a subordination approach, we treat the case of a stationary process with power law tail correlation function and diverging correlation time. We numerically test our findings, obtaining in both cases a good agreement with the analytical results. We notice that neither in the standard OU nor in the subordinated case a simple form of waiting time statistics like stretched-exponential or similar can be obtained while it is apparent that long time transient may shadow the final asymptotic behavior.