RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 Forthcoming seminars Seminar calendar List of seminars Archive by years Register a seminar Search RSS Forthcoming seminars

You may need the following programs to see the files

Principle Seminar of the Department of Probability Theory, Moscow State University
March 30, 2016 16:45–17:45, Moscow, MSU, auditorium 12-24

Some bounds for the maximum of a fractional Brownian motion

M. V. Zhitlukhin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We'll consider bounds for the expectation of the maximum of a fractional Brownian motion with Hurst parameter $H$ and its approximations by discrete-time processes. The main result shows that the difference of the expectations for the continuous-time process and a discrete approximation in n points can be estimated from above by a quantity of order $\sqrt{\log n}/n^H$. We'll also give a simple proof of that when $H$ tends to zero, the expectation of the maximum of a fractional Brownian motion can be bounded from above and below by quantities of order $1/\sqrt{H}$.