Work

Persistence probabilities of MA(1) sequences with Laplace innovations and $q$-deformed zigzag numbers

Year: 2025

Type: preprint

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 $q$-Pochhammer symbols or $q$-deformed analogues of Euler's zigzag numbers, respectively. Similarly, the generating functions of the persistence probabilities can be written in terms of $q$-analogues of the exponential function or the $q$-sine/$q$-cosine functions, respectively.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2512.14152

Authors: Aurzada, Frank, Raschel, Kilian

Institutions: Technische Universität Darmstadt, Centre National de la Recherche Scientifique, Université d'Angers

Language: English

Topic: Probability and Statistical Research

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Award: Conditioning and limit theorems for random walks and branching processes

OpenAlex ID: W4417466896

Cites: 2

Cited by: 4

Related to: 10