MA(1) processes with Laplace innovations conditioned to stay positive

Source abstract

We study a moving-average process with (not necessarily symmetric) Laplace innovations under the constraint of positivity. In the three nondegenerate parameter regimes $0 1$, and $θ 1$, and the dynamics are genuinely two-sided and governed by $q$-trigonometric functions for $θ<0$. In each case, the persistence exponent, sharp persistence asymptotics, the defining eigenfunction, and the unique invariant distribution are obtained explicitly.