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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.05670 |
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Table of Contents:
- We consider the persistence probabilities of an autoregressive chain of order one with continuous innovations. In the case of positive drifts, we show that these persistence probabilities are compound-geometric and satisfy a Baxter-Spitzer factorization generalizing that of the random walk. In the case of negative drifts, we exhibit a discrete Van Dantzig problem, which implies that the Baxter-Spitzer factorization never happens, except in a degenerate case. For positive drifts and log-concave innovations, we show that the first passage time in $(-\infty,0)$ has a log-convex distribution, whereas in the case of negative drifts and log-convex innovations on ${\mathbb R}^+$, it has a log-concave distribution. The case of the bi-exponential innovations is studied in detail, which leads for positive drifts to an additive factorization of the exponential law.