Convergence of an Adaptive Approximation Scheme for the Wiener Process

2010/02/02 by Mats Brodén, Brodén, Mats, Magnus Wiktorsson +1
Mathematics · #60F05 (Primary) #60G15 (Secondary) #FOS: Mathematics #Numerical methods in inverse problems #Probability (math.PR) #Statistical Methods and Inference #advanced mathematical theories #math.PR #msc:60F05 #msc:60G15

paper · pdf · doi:10.48550/arxiv.1002.0528

arxiv created 2010/02/02 · openalex publication_date 2010/02/02 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The problem of approximating/tracking the value of a Wiener process is considered. The discretization points are placed at times when the value of the process differs from the approximation by some amount, here denoted by eta. It is found that the limiting difference, as eta goes to 0, between the approximation and the value of the process normalized with eta converges in distribution to a triangularly distributed random variable.

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