Saddlepoint approximations and nonlinear boundary crossing probabilities of Markov random walks

DOI10.1214/aoap/1050689586zbMath1029.60058OpenAlexW1985826484MaRDI QIDQ1413670

Hock Peng Chan, Tze Leung Lai

Publication date: 17 November 2003

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

Full work available at URL: https://doi.org/10.1214/aoap/1050689586

zbMATH Keywords

large deviationMarkov additive processeschange-point detectionmaxima of random fields

Mathematics Subject Classification ID

Random fields (60G60) Central limit and other weak theorems (60F05) Discrete-time Markov processes on general state spaces (60J05) Stopping times; optimal stopping problems; gambling theory (60G40) Large deviations (60F10)

Related Items

Likelihood Ratio Identities and Their Applications to Sequential Analysis ⋮ A sequential Monte Carlo approach to computing tail probabilities in stochastic models ⋮ Importance Sampling for Generalized Likelihood Ratio Procedures in Sequential Analysis ⋮ Efficient importance sampling for Monte Carlo evaluation of exceedance probabilities ⋮ Discussion on “Change-Points: From Sequential Detection to Biology and Back” by David Siegmund ⋮ Sequential Change-Point Detection When the Pre- and Post-Change Parameters are Unknown ⋮ The stationary tail asymptotics in the GI/G/1-type queue with countably many background states ⋮ Asymptotic expansions on moments of the first ladder height in Markov random walks with small drift ⋮ Maxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices ⋮ Discussion on “Sequential detection/isolation of abrupt changes” by Igor V. Nikiforov ⋮ A Bayesian Approach to Sequential Surveillance in Exponential Families

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Markov additive processes. I: Eigenvalue properties and limit theorems
• Markov chains and stochastic stability
• Saddlepoint expansions for sums of Markov dependent variables on a continuous state space
• Statistical composition of high-scoring segments from molecular sequences
• Large deviations of uniformly recurrent Markov additive processes
• Approximate tail probabilities for the maxima of some random fields
• The ruin problem for finite Markov chains
• Large deviation lower bounds for arbitrary additive functionals of a Markov chain
• Boundary crossing probabilities for scan statistics and their applications to change-point detec\-tion
• Asymptotic approximations for error probabilities of sequential or fixed sample size tests in exponential families.
• Using the generalized likelihood ratio statistic for sequential detection of a change-point
• Sharp asymptotics of large deviations in \(\mathbb{R}^ d\)
• Identifying a large deviation rate function
• Asymptotic Properties of the Distribution of the Supremum of a Random Walk on a Markov Chain
• Differential Topology
• Central limit theorems and statistical inference for finite Markov chains
• A Local Limit Theorem for Nonlattice Multi-Dimensional Distribution Functions
• Extreme Values in the GI/G/1 Queue
• Saddlepoint Approximations in Statistics