# Advanced Methods in Mathematical Finance

1-4 September 2015
Angers - France
Europe/Paris timezone

## On the supremum of fractional Brownian motion and related processes

2 Sep 2015, 18:20
30m
Angers - France

### Speaker

Mikhail Zhitlukhin (Steklov Mathematical institute)

### Description

This paper studies the expected value of the supremum of fractional Brownian motion and related Gaussian processes. We obtain upper and lower bounds for the expected supremum and bounds for the approximation of the supremum of a continuous process by random walks. As corollaries, we obtain results on the structure of fractional Brownian motion when the Hurst parameter H tends to zero. This is a joint work with Konstantin Borovkov, Yulia Mishura and Alexander Novikov.

### Primary author

Mikhail Zhitlukhin (Steklov Mathematical institute)

 Slides