A universality class in Markovian persistence

Abstract

We consider the class of Markovian processes defined by the equation $\dd x /\dd t = -βx + \sum_k z_k δ(t-t_k)$. Such processes are encountered in systems (like coalescing systems) where dynamics creates discrete upward jumps at random instants $t_k$ and of random height $z_k$. We observe that the probability for these processes to remain above their mean value during an interval of time $T$ decays as $\exp{-θT}$ defining $θ$ as the persistence exponent. We show that $θ$ takes the value $β$ which thereby extends the well known result of the Gaussian noise case to a much larger class of non-Gaussian processes.