Search for dissertations about: "Fractional calculus"

Found 4 swedish dissertations containing the words Fractional calculus.

  1. 1. Some Extensions of Fractional Ornstein-Uhlenbeck Model : Arbitrage and Other Applications

    Author : José Igor Morlanes; Andriy Andreev; Hans Nyquist; Henrik Hult; Stockholms universitet; []
    Keywords : NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; fractional Ornstein-Uhlenbeck process; insider information; simulation embedding method; jump times; least-squares estimator; likelihood process; Ito calculus; Malliavin calculus; stochastic calculus; Statistics; statistik;

    Abstract : This doctoral thesis endeavors to extend probability and statistical models using stochastic differential equations. The described models capture essential features from data that are not explained by classical diffusion models driven by Brownian motion.New results obtained by the author are presented in five articles. READ MORE

  2. 2. The Finite Element Method for Fractional Order Viscoelasticity and the Stochastic Wave Equation

    Author : Fardin Saedpanah; Göteborgs universitet; Göteborgs universitet; Gothenburg University; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; finite element method; continuous Galerkin method; linear viscoelasticity; fractional calculus; fractional order viscoelasticity; weakly singular kernel; stability; a priori error estimate; a posteriori error estimate; stochastic wave equation; additive noise; Wiener process; strong convergence.;

    Abstract : This thesis can be considered as two parts. In the first part a hyperbolic type integro-differential equation with weakly singular kernel is considered, which is a model for dynamic fractional order viscoelasticity. In the second part, the finite element approximation of the linear stochastic wave equation is studied. READ MORE

  3. 3. Parabolic equations with low regularity

    Author : Magnus Fontes; Matematik LTH; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Matematik; Mathematics; Galerkin approximation.; low regularity; variational method; Hilbert transformation; fractional calculus; parabolic equations; quasilinear;

    Abstract : In this work we study a variational method for treating parabolic equations that yields new results for non-linear equations with low regularity on source and boundary data. We treat mainly strongly parabolic quasilinear equations and systems in divergence form. READ MORE

  4. 4. Abelian Extensions, Fractional Loop Group and Quantum Fields

    Author : Pedram Hekmati; Jouko Mickelsson; Christoph Schweigert; KTH; []
    Keywords : NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; Lie group extensions; Lie conformal algebras; gerbes; twisted K-theory; renormalization; anomalies; D-brane charges; variational complex; Mathematical physics; Matematisk fysik;

    Abstract : This thesis deals with the theory of Lie group extensions, Lie conformal algebras and twisted K-theory, in the context of quantum physics. These structures allow for a mathematically precise description of certain aspects of interacting quantum field theories. READ MORE