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fractional-integrals
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Fractional Brownian Motion and Application in Mathematical Finance
, M.Sc. Thesis Sharif University of Technology ; Zohuri Zangeneh, Bijan (Supervisor) ; Farhadi, Hamid Reza (Co-Advisor)
Abstract
Farctional Brownian motion (fBm) is a Gaussian Stochastic process B={B_t ∶t ≥0} With zero mean and Covariance function given by RH (t,s)=1/2 (t^2H+ S^2H-├|t-├ s┤|┤ 〖^2H〗) Where 0
Adaptive robust control of fractional-order swarm systems in the presence of model uncertainties and external disturbances
, Article IET Control Theory and Applications ; Volume 12, Issue 7 , 2018 , Pages 961-969 ; 17518644 (ISSN) ; Tavazoei, M. S ; Sharif University of Technology
Institution of Engineering and Technology
2018
Abstract
This study investigates the asymptotic swarm stabilisation of fractional-order swarm systems in the presence of two different kinds of model uncertainties and external disturbances while the upper bound of the uncertainties is a linear function of pseudo-states norms with unknown coefficients. To this end, first a fractional-integral sliding manifold is constructed and then an adaptive-robust sliding mode controller is designed to guarantee the asymptotic swarm stability in a fractional-order linear time-invariant swarm system. The stability analysis of the proposed control system is done based on the Lyapunov stability theorem. Using the proposed controller, the coefficients of the upper...
Upper and lower bounds for the maximum number of frequencies that can be generated by a class of fractional oscillators
, Article IEEE Transactions on Circuits and Systems I: Regular Papers ; Volume 66, Issue 4 , 2019 , Pages 1584-1593 ; 15498328 (ISSN) ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2019
Abstract
This paper deals with investigating the maximum number of frequencies generated by an oscillator in the case that a half number of integrators in the conventional dynamic structure of this oscillator are replaced by fractional integrators with an identical order. First, an upper bound for the maximum number of frequencies, which can exist in a steady state response of the oscillator, with respect to the number of integrators, is obtained. Then, on the basis of the recent advances in the field of determinant-based representations of bivariate polynomials, a lower bound is found for the maximum number of sinusoidal components in the steady state oscillations generated by the oscillator. A...
Analyzing the Relationship Between Tehran and Dubai Stock Exchange
, M.Sc. Thesis Sharif University of Technology ; Keshavarz Haddad, Gholamreza (Supervisor)
Abstract
One of the obvious features of financial markets is the spread of crisis across the markets, which is called contagion and realized in forms of return and volatility spillover. Using the daily data on the stock price from December 2006 through June 2010, this study aims to examine the presence and significance of these spillovers between Tehran and Dubai Stock Exchange, by a FIVECM technique. The FIVECM provides long-run equilibrium relationships between the returns in the markets and short-run dynamics of involved endogenous variables. Furthermore, it takes into account presence of fractionality in the time series’ integration. Our analytical framework, models the spillover effects in...
Nonlinear Modelling of Return and Volatility in IRANs Auto Industry
, M.Sc. Thesis Sharif University of Technology ; Keshavarz Hadad, Golam Reza (Supervisor)
Abstract
Long memory in assets return is important on the theoretical as well as the practical aspects and since it is a special form of nonlinear dynamics, in this study an ARFIMA model was used with the aim of considering the long memory in the return conditional average of automobile industry index. Then, due to the observation of ARCH effects, the simultaneous conditional average modeling and turbulences in the automotive industry index return using an ARFIMA-FIGARCH model was considered in the residuals of the best fitted model and results were that for modeling the returns and turbulences of automobile industry stocks which has a special long memory, FIGARCH will provide better and more...