Sökning: "covariance operator"

Visar resultat 1 - 5 av 12 avhandlingar innehållade orden covariance operator.

1. 1. Approximating Stochastic Partial Differential Equations with Finite Elements: Computation and Analysis

   Författare :Andreas Petersson; Chalmers tekniska högskola; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Lévy process; Lyapunov equation; white noise; finite element method; multilevel Monte Carlo; Monte Carlo; multiplicative noise; asymptotic mean square stability; stochastic heat equation; covariance operator; weak convergence; generalized Wiener process; numerical approximation; stochastic wave equation; Stochastic partial differential equations;

   Sammanfattning : Stochastic partial differential equations (SPDE) must be approximated in space and time to allow for the simulation of their solutions. In this thesis fully discrete approximations of such equations are considered, with an emphasis on finite element methods combined with rational semigroup approximations. LÄS MER

3. 2. Finite element approximation of the linear stochastic Cahn-Hilliard equation

   Författare :Ali Mesforush; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Cahn-Hilliard-Cook equation; finite element method; backward Euler method; error estimate; strong convergence; backward Euler method;

   Sammanfattning : The linearized Cahn-Hilliard-Cook equation is discretized in the spatial variables by a standard finite element method. Strong convergence estimates are proved under suitable assumptions on the covariance operator of the Wiener process, which is driving the equation. The backward Euler time stepping is also studied. LÄS MER

4. 3. On weak and strong convergence of numerical approximations of stochastic partial differential equations

   Författare :Fredrik Lindgren; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Additive noise; Cahn-Hilliard-Cook equation; Error estimate; Finite element; Hyperbolic equation; Parabolic equation; Rational approximation; Stochastic partial differential equation; Strong convergence; Truncation; Wiener process; Weak convergence; Weak convergence;

   Sammanfattning : This thesis is concerned with numerical approximation of linear stochastic partial differential equations driven by additive noise. In the first part, we develop a framework for the analysis of weak convergence and within this framework we analyze the stochastic heat equation, the stochastic wave equation, and the linearized stochastic Cahn-Hilliard, or the linearized Cahn-Hilliard-Cook equation. LÄS MER

5. 4. Construction of Representations of Commutation Relations by Linear Operators in Banach Spaces

   Författare :Domingos Djinja; Sergei Silvestrov; Samuel Lopes; Mälardalens universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics Applied Mathematics; matematik tillämpad matematik;

   Sammanfattning : This thesis is devoted to the construction and investigation of some properties of pairs of linear operators (A, B) (representations) satisfying commutation relations AB=BF(A), where F denotes certain polynomial. Commutation relations of this kind are called "covariance type" and finding their representations is equivalent to solving operator equations. LÄS MER

7. 5. Identification of viscoelastic materials and continuous-time stochastic systems

   Författare :Magnus Mossberg; Uppsala universitet; []
   Nyckelord :TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY; identification; viscoelastic; continuous-time; Signal processing; Signalbehandling; Signal Processing; Signalbehandling;

   Sammanfattning : Two system identification problems, identification of viscoelastic material properties and identification of continuous-time stochastic systems, are considered in the thesis. The viscoelastic material properties are characterised by the frequency-dependent complex modulus. LÄS MER