Paper
Persistence probabilities of MA(1) sequences with Laplace innovations and $q$-deformed zigzag numbers
Authors
Frank Aurzada, Kilian Raschel
Abstract
We study the persistence probabilities of a moving average process of order one with innovations that follow a Laplace distribution. The persistence probabilities can be computed fully explicitly in terms of classical combinatorial quantities like certain -Pochhammer symbols or -deformed analogues of Euler's zigzag numbers, respectively. Similarly, the generating functions of the persistence probabilities can be written in terms of -analogues of the exponential function or the -sine/-cosine functions, respectively.