Reference : Rate of Convergence for Discretization of Integrals with Respect to Fractional Browni...
 Document type : Scientific journals : Article Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/10993/13373
 Title : Rate of Convergence for Discretization of Integrals with Respect to Fractional Brownian Motion Language : English Author, co-author : Azmoodeh, Ehsan [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Viitasaari, Lauri [Aalto University] Publication date : 2013 Journal title : Journal of Theoretical Probability Peer reviewed : Yes (verified by ORBilu) Audience : International ISSN : 0894-9840 Keywords : [en] fractional Brownian motion ; tochastic integral ; rate of convergence Abstract : [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 $H - \frac{1}{2}$. Target : Researchers ; Professionals ; Students Permalink : http://hdl.handle.net/10993/13373

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