Adaptive Approximation of the Minimum of Brownian Motion
  We study the error in approximating the minimum of a Brownian motion on the unit interval based on finitely many point evaluations. We construct an algorithm that adaptively chooses the points at which to evaluate the Brownian path. In contrast to the $1/2$ convergence rate of optimal nonadaptive algorithms, the proposed adaptive algorithm converges at an arbitrarily high polynomial rate. 
James M. Calvin and Mario Hefter and Andr\'e Herzwurm
math.PR