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• W2783252188 abstract "For a class of one-dimensional autoregressive processes $(X_n)$ we consider the tail behaviour of the stopping time $T_0=min lbrace ngeq 1: X_nleq 0 rbrace$. We discuss existing general analytical approaches to this and related problems and propose a new one, which is based on a renewal-type decomposition for the moment generating function of $T_0$ and on the analytical Fredholm alternative. Using this method, we show that $mathbb{P}_x(T_0=n)sim V(x)R_0^n$ for some $0<R_0<1$ and a positive $R^{-1}_0$-harmonic function $V$. Further we prove that our conditions on the tail behaviour of the innovations are sharp in the sense that fatter tails produce non-exponential decay factors." @default.
• W2783252188 created "2018-01-26" @default.
• W2783252188 creator A5054817942 @default.
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• W2783252188 date "2018-01-13" @default.
• W2783252188 modified "2023-10-01" @default.
• W2783252188 title "Persistence of one-dimensional AR(1)-sequences" @default.
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• W2783252188 hasPublicationYear "2018" @default.
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