The rate of convergence for increments of a Brownian motion in Hölder norm

Yonghong Liu, Luoqing Li and Chenggao Wan

Statistics & Probability Letters, 2009, vol. 79, issue 12, 1463-1472

Abstract: We investigate the convergence of the functional limit for increments of a Brownian motion in Hölder norm. The rate of convergence in the functional limit for increments of a d-dimensional Brownian motion is derived. The main tool in the proof is large deviation and small deviation for Brownian motion in Hölder topology.

Date: 2009
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