Asymptotic expansions on moments of the first ladder height in Markov random walks with small drift

DOI10.1239/aap/1189518640zbMath1127.60084OpenAlexW2092109088MaRDI QIDQ5426471

Cheng-Der Fuh

Publication date: 12 November 2007

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/aap/1189518640

zbMATH Keywords

Poisson equationovershootboundary crossing probabilityladder height distributionMarkov-dependent Wald martingaleuniform Markov renewal theory

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Markov renewal processes, semi-Markov processes (60K15) Renewal theory (60K05)

Related Items

Approximation formulas for the moments of the boundary functional of a Gaussian random walk with positive drift by using Siegmund's formula, Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes

Cites Work

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• Markov additive processes. I: Eigenvalue properties and limit theorems
• On some boundary crossing problems for Gaussian random walks
• Markov chains and stochastic stability
• Complete corrected diffusion approximations for the maximum of a random walk
• Sequential analysis. Tests and confidence intervals
• Approximate tail probabilities for the maxima of some random fields
• Large deviations for boundary crossing probabilities
• The ruin problem for finite Markov chains
• On moments of the first ladder height of random walks with small drift
• Renewal theory for functionals of a Markov chain with general state space
• Ladder heights, Gaussian random walks and the Riemann zeta function
• SPRT and CUSUM in hidden Markov models
• Saddlepoint approximations and nonlinear boundary crossing probabilities of Markov random walks
• Renewal theory for functionals of a Markov chain with compact state space.
• Poisson equation, moment inequalities and quick convergence for Markov random walks.
• Uniform Markov renewal theory and ruin probabilities in Markov random walks.
• Limits of first passage times to rare sets in regenerative processes
• Asymptotic expansions in multidimensional Markov renewal theory and first passage times for Markov random walks
• Limit theorems for first-passage times in linear and non-linear renewal theory
• An Asymptotic Analysis of a Queueing System with Markov-Modulated Arrivals
• Corrected diffusion approximations in certain random walk problems
• Asymptotic Properties of the Distribution of the Supremum of a Random Walk on a Markov Chain
• Wald's equations, first passage times and moments of ladder variables in Markov random walks
• Corrected Diffusion Approximations for Ruin Probabilities in a Markov Random Walk
• Applied Probability and Queues
• Risk theory in a Markovian environment
• On Excess Over the Boundary