Persistence of autoregressive sequences with logarithmic tails

DOI10.1214/22-EJP879MaRDI QIDQ2105158

Vitali Wachtel, Martin Kolb, Denis Denisov, Günter Hinrichs

Publication date: 8 December 2022

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.14772

zbMATH Keywords

harmonic functionrandom walkexit timeconditioned process

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Stopping times; optimal stopping problems; gambling theory (60G40) Functional limit theorems; invariance principles (60F17)

Related Items (1)

Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials

Cites Work

• Tail asymptotics for the supremum of a random walk when the mean is not finite
• Exponential functionals of Lévy processes
• Conditioned limit theorems for some null recurrent Markov processes
• Asymptotics for sums of random variables with local subexponential behaviour
• Recurrence and transience of contractive autoregressive processes and related Markov chains
• Persistence exponents in Markov chains
• Persistence exponents via perturbation theory: AR(1)-processes
• Weak convergence of positive self-similar Markov processes and overshoots of Lévy processes
• Functional limit theorems for divergent perpetuities in the contractive case
• SOME PROPERTIES OF A RANDOM LINEAR DIFFERENCE EQUATION1
• Subexponential distributions and integrated tails
• On a general random exchange model
• Recurrence properties of autoregressive processes with super-heavy-tailed innovations
• Null recurrence and transience of random difference equations in the contractive case
• Semi-stable Markov processes. I

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