Ceren Vardar, Hatice Cakar
Published 2013-02-08Version 1
In this study, it is theoretically proven that the expected value of maximum loss of fractional Brownian motion (fBm) up to time 1 with Hurst parameter $[1/2,1)$ is bounded above by $2/\sqrt{\pi}$ and below by $1/\sqrt{\pi}$. This result is generalized for fBm with $H\in[1/2,1)$ up to any fixed time, $t$. This also leads us to the bounds related to the distribution of maximum loss of fBm. As numerical study some lower bounds on the expected value of maximum loss of fBm up to time 1 are obtained by discretization. Simulation study is conducted with Cholesky method. Finally, comparison of the established bounds with simulation results is given.
Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes
Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion
Rate of convergence for discretization of integrals with respect to Fractional Brownian motion
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