Approximation formulas for the moments of the boundary functional of a Gaussian random walk with positive drift by using Siegmund's formula

DOI10.1080/03610918.2018.1468449OpenAlexW2889759043MaRDI QIDQ5087544

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Publication date: 1 July 2022

Published in: Communications in Statistics - Simulation and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610918.2018.1468449

zbMATH Keywords

Gaussian random walk meta-modeling ladder height boundary functional positive drift Dynkin principle Reimann zeta-function

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Markov renewal processes, semi-Markov processes (60K15) Limit theorems in probability theory (60F99)

Cites Work

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Exact expressions for the moments of ladder heights
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Modes of a Gaussian random walk
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Asymptotic expansions for the moments of a semi-Markovian random walk with exponential distributed interference of chance
Asymptotic approach for a renewal-reward process with a general interference of chance
Weak Convergence Theorem for Ergodic Distribution of Stochastic Processes with Discrete Interference of Chance and Generalized Reflecting Barrier
Corrected diffusion approximations in certain random walk problems
Asymptotics for the moments of the overshoot and undershoot of a random walk
Asymptotic expansions on moments of the first ladder height in Markov random walks with small drift
On the stationary characteristics of the extended model of type (s,S) with Gaussian distribution of summands

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