If you need an accessible version of this item please contact JSTOR User Support

Limit Theorems for First-Passage Times in Linear and Non-Linear Renewal Theory

S. P. Lalley
Advances in Applied Probability
Vol. 16, No. 4 (Dec., 1984), pp. 766-803
DOI: 10.2307/1427340
Stable URL: http://www.jstor.org/stable/1427340
Page Count: 38
  • Download PDF
  • Cite this Item

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support
Limit Theorems for First-Passage Times in Linear and Non-Linear Renewal Theory
Preview not available

Abstract

A local limit theorem for P{τ a=n, Sτ a -a≤ x} is obtained, where τ a is the first time a random walk Sn with positive drift exceeds a. Applications to large-deviation probabilities and to the crossing of a non-linear boundary are given.

Page Thumbnails

  • Thumbnail: Page 
766
    766
  • Thumbnail: Page 
767
    767
  • Thumbnail: Page 
768
    768
  • Thumbnail: Page 
769
    769
  • Thumbnail: Page 
770
    770
  • Thumbnail: Page 
771
    771
  • Thumbnail: Page 
772
    772
  • Thumbnail: Page 
773
    773
  • Thumbnail: Page 
774
    774
  • Thumbnail: Page 
775
    775
  • Thumbnail: Page 
776
    776
  • Thumbnail: Page 
777
    777
  • Thumbnail: Page 
778
    778
  • Thumbnail: Page 
779
    779
  • Thumbnail: Page 
780
    780
  • Thumbnail: Page 
781
    781
  • Thumbnail: Page 
782
    782
  • Thumbnail: Page 
783
    783
  • Thumbnail: Page 
784
    784
  • Thumbnail: Page 
785
    785
  • Thumbnail: Page 
786
    786
  • Thumbnail: Page 
787
    787
  • Thumbnail: Page 
788
    788
  • Thumbnail: Page 
789
    789
  • Thumbnail: Page 
790
    790
  • Thumbnail: Page 
791
    791
  • Thumbnail: Page 
792
    792
  • Thumbnail: Page 
793
    793
  • Thumbnail: Page 
794
    794
  • Thumbnail: Page 
795
    795
  • Thumbnail: Page 
796
    796
  • Thumbnail: Page 
797
    797
  • Thumbnail: Page 
798
    798
  • Thumbnail: Page 
799
    799
  • Thumbnail: Page 
800
    800
  • Thumbnail: Page 
801
    801
  • Thumbnail: Page 
802
    802
  • Thumbnail: Page 
803
    803