A nonlinear renewal theory

DOI10.1214/aop/1176991788zbMath0643.60067OpenAlexW2055760790MaRDI QIDQ1102046

Cun-Hui Zhang

Publication date: 1988

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176991788

zbMATH Keywords

uniform integrabilityperturbed random walkrenewal theoremsfirst passage time across a nonlinear boundary

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Stopping times; optimal stopping problems; gambling theory (60G40) Sequential statistical analysis (62L10) Sequential estimation (62L12) Optimal stopping in statistics (62L15) Renewal theory (60K05)

Related Items (14)

Nonlinear renewal theory for Markov random walks ⋮ First passage times for perturbed random walks ⋮ Nonlinear renewal theory under growth conditions ⋮ On the first passage time of the parabolic boundary by the Markov random walk ⋮ A nonlinear parking problem ⋮ A uniform renewal theorem ⋮ Credit Risk Propagation in Structural-Form Models ⋮ The key renewal theorem for a transient Markov chain ⋮ Asymptotic operating characteristics of an optimal change point detection in hidden Markov models ⋮ Stopped diffusion processes: boundary corrections and overshoot ⋮ Approximations to expected stopping times with applications to sequential estimation ⋮ On a fundamental identity for stopping times and its application to risk theory ⋮ The probability of exceeding a high boundary on a random time interval for a heavy-tailed random walk ⋮ Nonparametric change-point detection for two populations

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