Overshoots over curved boundaries

R. A. Doney, P. S. Griffin

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We consider the asymptotic behaviour of a random walk when it exits from a symmetric region of the form {(x, n) : |x| ≤ rnb} as r → ∞. In order to be sure that this actually occurs, we treat only the case where the power b lies in the interval [0, 1/2), and we further assume a condition that prevents the probability of exiting at either boundary tending to 0. Under these restrictions we establish necessary and sufficient conditions for the pth moment of the overshoot to be O(rq), and for the overshoot to be tight, as r → ∞.

Original languageEnglish (US)
Pages (from-to)417-448
Number of pages32
JournalAdvances in Applied Probability
Volume35
Issue number2
DOIs
StatePublished - Jun 1 2003

Keywords

  • Exit times
  • Moments of overshoots
  • Random walks
  • Relative stability
  • Tightness

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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