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 Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Boundary Crossing Probability for Brownian Motion and General Boundaries

Liqun Wang and Klaus Pötzelberger
Journal of Applied Probability
Vol. 34, No. 1 (Mar., 1997), pp. 54-65
DOI: 10.2307/3215174
Stable URL: http://www.jstor.org/stable/3215174
Page Count: 12
  • Read Online (Free)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Boundary Crossing Probability for Brownian Motion and General Boundaries
Preview not available

Abstract

An explicit formula for the probability that a Brownian motion crosses a piecewise linear boundary in a finite time interval is derived. This formula is used to obtain approximations to the crossing probabilities for general boundaries which are the uniform limits of piecewise linear functions. The rules for assessing the accuracies of the approximations are given. The calculations of the crossing probabilities are easily carried out through Monte Carlo methods. Some numerical examples are provided.

Page Thumbnails

  • Thumbnail: Page 
54
    54
  • Thumbnail: Page 
55
    55
  • Thumbnail: Page 
56
    56
  • Thumbnail: Page 
57
    57
  • Thumbnail: Page 
58
    58
  • Thumbnail: Page 
59
    59
  • Thumbnail: Page 
60
    60
  • Thumbnail: Page 
61
    61
  • Thumbnail: Page 
62
    62
  • Thumbnail: Page 
63
    63
  • Thumbnail: Page 
64
    64
  • Thumbnail: Page 
65
    65