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  4. On the expected uniform error of Brownian motion approximated by the Lévy-Ciesielski construction
 
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2024
Journal Article
Title

On the expected uniform error of Brownian motion approximated by the Lévy-Ciesielski construction

Abstract
The Brownian bridge or Lévy-Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. We focus on the uniform error. In particular, we show constructively that at level N, at which there are d=2N 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), matching the known orders. We apply the results to an option pricing example.
Author(s)
Brown, Bruce
University of New South Wales, School of Mathematics and Statistics
Griebel, Michael  
Universität Bonn, Institut für Numerische Simulation
Kuo, Frances Y.
University of New South Wales, School of Mathematics and Statistics
Sloan, Ian H.
University of New South Wales, School of Mathematics and Statistics
Journal
Bulletin of the Australian Mathematical Society  
Open Access
DOI
10.1017/S0004972723000850
Language
English
Fraunhofer-Institut für Algorithmen und Wissenschaftliches Rechnen SCAI  
Keyword(s)
  • Brownian motion

  • Brownian bridge

  • Lévy-Ciesielski construction

  • expected uniform error

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