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A coupling proof of weak convergence
Published online by Cambridge University Press: 14 July 2016
Abstract
Weak convergence to reflected Brownian motion is deduced for certain upwardly drifting random walks by coupling them to a simple reflected random walk. The argument is quite elementary, and also gives the right conditions on the drift. A similar argument works for a corresponding continuous-time problem.
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- Copyright © Applied Probability Trust 1985