Frank Aurzada

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

We study a moving-average process with (not necessarily symmetric) Laplace innovations under the constraint of positivity. In the three nondegenerate parameter regimes $0<\theta<1$, $\theta>1$, and $\theta<0$, we prove convergence of the conditioned finite-dimensional distributions and identify the limit as a Doob $h$-...