We investigate how the correlation properties of a stationary Markovian stochastic process aﬀect its First Passage Time Distribution (FPTD). With explicit examples, in this paper we show that the tail of the ﬁrst passage time distribution crucially depends on the correlation properties of the process and it is independent of its stationary distribution. When the process includes an inﬁnite set of time-scales bounded from above, the FPTD shows tails modulated by some exponential decay. In the case when the process is power-law correlated the FPTD shows power-law tails 1/t^ν and therefore the moments ⟨t^n⟩ of the FPTD are ﬁnite only when n < ν − 1. The existence of an inﬁnite and unbounded set of time-scales is a necessary but not suﬃcient condition in order to observe power-law tails in the FPTD. Finally, we give a general result connecting the FPTD of an additive stochastic processes x(t) to the FPTD of a generic process y(t) related by a coordinate transformation y = f (x) to the ﬁrst one.
|Number of pages||6|
|Publication status||Published - 2010|