Brown, Bruce; Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H.: On the expected uniform error of Brownian motion approximated by the Lévy-Ciesielski construction. In: INS Preprints, 2301.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11576
@unpublished{handle:20.500.11811/11576,
author = {{Bruce Brown} and {Michael Griebel} and {Frances Y. Kuo} and {Ian H. Sloan}},
title = {On the expected uniform error of Brownian motion approximated by the Lévy-Ciesielski construction},
publisher = {Institut für Numerische Simulation},
year = 2023,
month = apr,

INS Preprints},
volume = 2301,
note = {It is known that the Brownian bridge or Lévy-Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. In the present article the focus is on the uniform error. In particular, we show constructively that at level N, at which there are d = 2^N points evaluated on the Brownian path, the uniform error and its square, and the uniform error of geometric Brownian motion, have upper bounds of order O ( (ln d / d)^(1/2) ), matching the known orders. We apply the results to an option pricing example.},
url = {https://hdl.handle.net/20.500.11811/11576}
}

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