Stochastic Calculus with Respect to Fractional Brownian Motion

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Najafi, Alireza | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 44050 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zohuri Zangeneh, Bijan
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 work, we prove a formula for Gaussian process in general and it is show Stratonovich integral is non-random integral in the calculation
Keywords:
Brownian motion ; Malliavin Calculus ; Herest Index

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