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Principle Seminar of the Department of Probability Theory, Moscow State University
March 30, 2016 16:45, 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

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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 $1/\sqrt{H}$.

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