Janssen, A. J. E. M; Van Leeuwaarden, J. S. H. Equidistant sampling for the maximum of a Brownian motion with drift on a finite horizon. (English) Zbl 1191.60060 Electron. Commun. Probab. 14, 143-150 (2009). Summary: A Brownian motion observed at equidistant sampling points renders a random walk with normally distributed increments. For the difference between the expected maximum of the Brownian motion and its sampled version, an expansion is derived with coefficients in terms of the drift, the Riemann zeta function and the normal distribution function. Cited in 1 ReviewCited in 4 Documents MSC: 60G50 Sums of independent random variables; random walks 60J65 Brownian motion Keywords:Gaussian random walk; maximum; Riemann zeta function; Euler-MacLaurin summation; equidistant sampling of Brownian motion; finite horizon PDF BibTeX XML Cite \textit{A. J. E. M Janssen} and \textit{J. S. H. Van Leeuwaarden}, Electron. Commun. Probab. 14, 143--150 (2009; Zbl 1191.60060) Full Text: DOI EuDML EMIS OpenURL