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|a (JST)20443542
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|a eng
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|2 MSC
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|a Fuh, Cheng-Der
|e verfasserin
|4 aut
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|a Asymptotic Expansions on Moments of the First Ladder Height in Markov Random Walks with Small Drift
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|c 2007
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|a Text
|b txt
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|a Computermedien
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|a Let $\{(X_{n},\ S_{n}),\ n\geq 0\}$ be a Markov random walk in which $X_{n}$ takes values in a general state space and $S_{n}$ takes values on the real line ℝ. In this paper we present some results that are useful in the study of asymptotic approximations of boundary crossing problems for Markov random walks. The main results are asymptotic expansions on moments of the first ladder height in Markov random walks with small positive drift. In order to establish the asymptotic expansions we study a uniform Markov renewal theorem, which relates to the rate of convergence for the distribution of overshoot, and present an analysis of the covariance between the first passage time and the overshoot.
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|a Copyright 2007 Applied Probability Trust
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|a Boundary crossing probability
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|a ladder height distribution
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|a Markov-dependent Wald martingale
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|a overshoot
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| 650 |
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|a Poisson equation
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| 650 |
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|a uniform Markov renewal theory
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| 650 |
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4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Random walk
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| 650 |
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4 |
|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
|x Stochastic processes
|x Markov processes
|x Markov chains
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| 650 |
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4 |
|a Mathematics
|x Mathematical procedures
|x Approximation
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| 650 |
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4 |
|a Mathematics
|x Pure mathematics
|x Probability theory
|x Probabilities
|x Transition probabilities
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| 650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Calculus
|x Differential calculus
|x Differential equations
|x Partial differential equations
|x Elliptic differential equations
|x Poisson equation
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| 650 |
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4 |
|a Applied sciences
|x Computer science
|x Artificial intelligence
|x Machine learning
|x Perceptron convergence procedure
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| 650 |
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4 |
|a Applied sciences
|x Systems science
|x Systems theory
|x Dynamical systems
|x Ergodic theory
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| 650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Distribution functions
|x Probability distributions
|x Mathematical moments
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| 650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
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| 650 |
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4 |
|a Mathematics
|x Pure mathematics
|x Algebra
|x Coefficients
|x General Applied Probability
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| 655 |
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|a research-article
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|i Enthalten in
|t Advances in Applied Probability
|d Applied Probability Trust
|g 39(2007), 3, Seite 826-852
|w (DE-627)269247009
|w (DE-600)1474602-5
|x 00018678
|7 nnns
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|g volume:39
|g year:2007
|g number:3
|g pages:826-852
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|u https://www.jstor.org/stable/20443542
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|d 39
|j 2007
|e 3
|h 826-852
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