Sökning: "stochastic heat equation"

Visar resultat 1 - 5 av 12 avhandlingar innehållade orden stochastic heat equation.

  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. Topics in Simulation and Stochastic Analysis

    Författare :Mikael Signahl; Matematisk statistik; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Matematik; stochastic heat equation; stochastic wave equation; error rates; truncated Levy process; discontinuities; optimal decay rate; digital communication system;

    Sammanfattning : Paper A investigates how to simulate a differentiated mean in cases where interchanging differentiation and expectation is not allowed. Three approaches are available, finite differences (FD's), infinitesimal perturbation analysis (IPA) and the likelihood ratio score function (LRSF) method. LÄS MER

  4. 3. A weak space-time formulation for the linear stochastic heat equation

    Författare :Matteo Molteni; Göteborgs universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Inf-sup theory; Stochastic heat equation; Petrov-Galerkin; Finite element; Crank-Nicolson; Quasi-optimality; Finite element;

    Sammanfattning : The topic covered in this thesis is the introduction of a new formulation for the linear stochastic heat equation driven by additive noise, based on the space-time variational formulation for its deterministic counterpart. Having a variational formulation allows the use of the so called inf-sup theory in order to obtain results of existence and uniqueness in a relatively simple way. LÄS MER

  5. 4. 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

  7. 5. Selected Topics in Mathematical Modelling: Machine Learning and Tugs-of-War

    Författare :Carmina Fjellström; Kaj Nyström; Andrea Pascucci; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Machine learning; Neural networks; LSTM; Financial forecasting; Time series analysis; Stochastic gradient descent; Diffusion map; Dimension reduction; Tug-of-war games; Fractional heat operator; Mean value property; Infinity fractional heat operators; Dynamic programming principle; p-Laplacian; Infinity Laplacian; Kolmogorov equation; Stochastic games; Viscosity solutions; Tillämpad matematik och statistik; Applied Mathematics and Statistics;

    Sammanfattning : This thesis concerns selected topics in mathematical modelling, namely in machine learning and stochastic games called tugs-of-war. It consists of four scientific articles. The first and second are about machine learning topics, while the third and fourth articles are about tug-of-war games. LÄS MER