Stochastic Calculus with Respect to Fractional Brownian Motion, M.Sc. Thesis Sharif University of Technology ; Zohuri Zangeneh, Bijan (Supervisor)
Abstract
The aim of this thesis is to examine different perspectives on stochastic integrals of fractional Brownian motion. We examine two main perspectives. In the first perspective, we present Mallivan idea in general and in the second idea Riemannian calculus perspective in briefly.In first, we explain basic idea in Mallivan calculus for example Hida spaces, operator δ and we try as ordinary Brownian motion, in this work follow the same trend. The next step, as conventional stochastic integrals Martingle Dob inequality, we introduce torques to find an upper bound for this integral.In Mallivan perspective, we are looking for a formula to maintain Ito formula in a certain space.In the following...
Cataloging briefStochastic Calculus with Respect to Fractional Brownian Motion, M.Sc. Thesis Sharif University of Technology ; Zohuri Zangeneh, Bijan (Supervisor)
Abstract
The aim of this thesis is to examine different perspectives on stochastic integrals of fractional Brownian motion. We examine two main perspectives. In the first perspective, we present Mallivan idea in general and in the second idea Riemannian calculus perspective in briefly.In first, we explain basic idea in Mallivan calculus for example Hida spaces, operator δ and we try as ordinary Brownian motion, in this work follow the same trend. The next step, as conventional stochastic integrals Martingle Dob inequality, we introduce torques to find an upper bound for this integral.In Mallivan perspective, we are looking for a formula to maintain Ito formula in a certain space.In the following...
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