Improving Brownian approximations for boundary crossing problems
arXiv:1301.7625 · doi:10.3150/11-BEJ396
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.
Published in at http://dx.doi.org/10.3150/11-BEJ396 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)