Access

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

On Excess Over the Boundary

Gary Lorden
The Annals of Mathematical Statistics
Vol. 41, No. 2 (Apr., 1970), pp. 520-527
Stable URL: http://www.jstor.org/stable/2239350
Page Count: 8
  • Read Online (Free)
  • Download ($19.00)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
On Excess Over the Boundary
Preview not available

Abstract

A random walk, {Sn}∞ n=0, having positive drift and starting at the origin, is stopped the first time $S_n > t \geqq 0$. The present paper studies the "excess," Sn - t, when the walk is stopped. The main result is an upper bound on the mean of the excess, uniform in t. Through Wald's equation, this gives an upper bound on the mean stopping time, as well as upper bounds on the average sample numbers of sequential probability ratio tests. The same elementary approach yields simple upper bounds on the moments and tail probabilities of residual and spent waiting times of renewal processes.

Page Thumbnails

  • Thumbnail: Page 
520
    520
  • Thumbnail: Page 
521
    521
  • Thumbnail: Page 
522
    522
  • Thumbnail: Page 
523
    523
  • Thumbnail: Page 
524
    524
  • Thumbnail: Page 
525
    525
  • Thumbnail: Page 
526
    526
  • Thumbnail: Page 
527
    527