Bernoulli

  • Bernoulli
  • Volume 19, Number 1 (2013), 137-153.

Improving Brownian approximations for boundary crossing problems

Robert Keener

Full-text: Open access

Abstract

Donsker’s theorem shows that random walks behave like Brownian motion in an asymptotic sense. This result can be used to approximate expectations associated with the time and location of a random walk when it first crosses a nonlinear boundary. In this paper, correction terms are derived to improve the accuracy of these approximations.

Article information

Source
Bernoulli, Volume 19, Number 1 (2013), 137-153.

Dates
First available in Project Euclid: 18 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1358531744

Digital Object Identifier
doi:10.3150/11-BEJ396

Mathematical Reviews number (MathSciNet)
MR3019489

Zentralblatt MATH identifier
1270.60053

Keywords
asymptotic expansion Donsker’s theorem excess over the boundary random walk stopping times

Citation

Keener, Robert. Improving Brownian approximations for boundary crossing problems. Bernoulli 19 (2013), no. 1, 137--153. doi:10.3150/11-BEJ396. https://projecteuclid.org/euclid.bj/1358531744


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