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

Improving Brownian approximations for boundary crossing problems

Robert Keener

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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.

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

First available in Project Euclid: 18 January 2013

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


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

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