Survival probabilities of autoregressive processes

2012/07/16 by Christoph Baumgarten, Baumgarten, Christoph · 2 citations
Computer Science · Decision Sciences · Mathematics · #60G15 #60G50 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1207.3610

openalex publication_date 2012/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given an autoregressive process X of order p (i.e. X_n = a₁ X_n-1 + ...+ a_p X_np + Y_n where the random variables Y₁, Y₂, ... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a constant barrier up to time N (survival or persistence probability). Depending on the coefficients a₁,...,a_p and the distribution of Y₁, we state conditions under which the survival probability decays polynomially, faster than polynomially or converges to a positive constant. Special emphasis is put on AR(2) processes.

Citations

• Survival probabilities of weighted random walks
• Association of Random Variables, with Applications

Cited by

• Persistence probabilities of MA(1) sequences with Laplace innovations and q-deformed zigzag numbers
• Persistence probabilities for MA(1) sequences with uniform innovations

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