Reference : Rate of Convergence for Discretization of Integrals with Respect to Fractional Browni...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/13373
Rate of Convergence for Discretization of Integrals with Respect to Fractional Brownian Motion
English
Azmoodeh, Ehsan mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Viitasaari, Lauri [Aalto University]
2013
Journal of Theoretical Probability
Yes (verified by ORBilu)
International
0894-9840
[en] fractional Brownian motion ; tochastic integral ; rate of convergence
[en] In this article, an uniform discretization of stochastic integrals $\int_{0}^{1} f'_-(B_t)\ud B_t$, where $B_t$ denotes the fractional Brownian motion with Hurst parameter $H \in (\frac{1}{2},1)$, for a large class of convex functions $f$ is considered. In $\big[$\cite{a-m-v}, Statistics \& Decisions, \textbf{27}, 129-143$\big]$, for any convex function $f$, the almost sure convergence of uniform discretization to such stochastic integral is proved. Here we prove $L^r$- convergence of uniform discretization to stochastic integral. In addition, we obtain a rate of convergence. It turns out that the rate of convergence can be brought arbitrary close to $H - \frac{1}{2}$.
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/13373

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