Persistence probabilities of AR(1) chains with continuous innovations are compound-geometric for positive drifts and admit Baxter-Spitzer factorization, but not for negative drifts except degenerately; first-passage times are log-convex or log-concave according to innovation shape and drift sign.
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Persistence probabilities of autoregressive chains with continuous innovations
Persistence probabilities of AR(1) chains with continuous innovations are compound-geometric for positive drifts and admit Baxter-Spitzer factorization, but not for negative drifts except degenerately; first-passage times are log-convex or log-concave according to innovation shape and drift sign.