Optimal Pointwise Approximation of Sdes Based on Brownian Motion at Discrete Points

Abstract

We study pathwise approximation of scalar stochastic differential equations at a single point. We provide the exact rate of convergence of the minimal errors that can be achieved by arbitrary numerical methods that are based (in a measurable way) on a finite number of sequential observations of the driving Brownian motion. The resulting lower error bounds… (More)

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