PreprintCC BY-NC-ND 4.0HAL
Persistence probabilities of MA(1) sequences with Laplace innovations and q-deformed zigzag numbers
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.
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BibTeX
@misc{aurzada2026persistence,
title = {{Persistence probabilities of MA(1) sequences with Laplace innovations and q-deformed zigzag numbers}},
author = {Frank Aurzada and Kilian Raschel},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2512.14152},
url = {https://hal.science/hal-05844982v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Persistence probabilities of MA(1) sequences with Laplace innovations and q-deformed zigzag numbers
AU - Frank Aurzada
AU - Kilian Raschel
PY - 2026
DA - 2026/10/30
PB - HAL
DO - 10.48550/arxiv.2512.14152
UR - https://hal.science/hal-05844982v1
AB - 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.
ER -