Overshoots over curved boundaries. II

R. A. Doney, P. S. Griffin

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We continue the study of the asymptotic behaviour a random walk when it exits from a symmetric region of the form {(x,n): x ≤ rnb} as r → ∞, which was begun in Part I of this work. In contrast to that paper, we are interested in the case where the probability of exiting at the upper boundary tends to 1. In this scenario we treat the case where the power b lies in the interval [0, 1], and we establish necessary and sufficient conditions for the overshoot to be relatively stable in probability (except for the case b = 1/2), and for the pth moment of the overshoot to be 0 (rq) as r → ∞.

Original languageEnglish (US)
Pages (from-to)1148-1174
Number of pages27
JournalAdvances in Applied Probability
Volume36
Issue number4
DOIs
StatePublished - Dec 1 2004

Keywords

  • Exit time
  • Moment of overshoot
  • Power-law boundary
  • Random walk
  • Relative stability

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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