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1 results

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

  • Part of
  • Cheng-Der Fuh
  • Journal:
    Advances in Applied Probability / Volume 39 / Issue 3 / September 2007
    Published online by Cambridge University Press:
    01 July 2016, pp. 826-852
    Print publication:
    September 2007
    • Article
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  • Let {(Xn, Sn), n ≥ 0} be a Markov random walk in which Xn takes values in a general state space and Sn 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.