An MA(1) process with uniform innovations conditioned to stay positive converges to an explicit Doob h-transform with phase-dependent transition kernel when the coupling parameter lies in [-1,1).
Persistence probabilities of MA(1) sequences with Laplace innovations andq-deformed zigzag numbers
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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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MA(1) processes with uniform innovations conditioned to stay positive in the non-expanding regime
An MA(1) process with uniform innovations conditioned to stay positive converges to an explicit Doob h-transform with phase-dependent transition kernel when the coupling parameter lies in [-1,1).
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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.