Persistence probabilities of MA(1) sequences with Laplace innovations and $q$-deformed zigzag numbers
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908714551738368 |
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| author | Aurzada, Frank Raschel, Kilian |
| author_facet | Aurzada, Frank Raschel, Kilian |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_14152 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Persistence probabilities of MA(1) sequences with Laplace innovations and $q$-deformed zigzag numbers Aurzada, Frank Raschel, Kilian Probability Combinatorics 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. |
| title | Persistence probabilities of MA(1) sequences with Laplace innovations and $q$-deformed zigzag numbers |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2512.14152 |