Sökning: "stochastic differential equation"

Visar resultat 1 - 5 av 66 avhandlingar innehållade orden stochastic differential equation.

  1. 1. Numerical analysis and simulation of stochastic partial differential equations with white noise dispersion

    Författare :André Berg; David Cohen; Per Åhag; Guillaume Dujardin; Ludovic Goudenège; Umeå universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; stochastic partial differential equation; mathematics; numerical analysis; numerical scheme; time integrator; convergence analysis; blowup; critical exponent; nonlinear Schrödinger equation; Manakov equation; Benjamin-Bona-Mahony equation; BBM equation; stochastic; random; dispersion; white noise dispersion; finite difference; pseudospectral; code; matlab; exponential integrator; splitting integrator; convergence in probability; Mathematics; matematik; Numerical Analysis; numerisk analys;

    Sammanfattning : This doctoral thesis provides a comprehensive numerical analysis and exploration of several stochastic partial differential equations (SPDEs). More specifically, this thesis investigates time integrators for SPDEs with white noise dispersion. LÄS MER

  3. 2. 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

  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. Contributions to Numerical Solution of Stochastic Differential Equations

    Författare :Anders Muszta; Göteborgs universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; adaptive method; change of time; CIR model; CKLS model; convergence order; Euler method; heavy-tailed SDE; hyperbolic SDE; geometric integration; global Lipschitz condition; Levy process; Lie group method; local Lipschitz condition; local martingales; mean reversion; Milstein method; numerical method; semimartingale; stochastic differential equation; stochastic Taylor expansion; strong approximation; symplectic integration; volatility induced stationarity; waveform relaxation; volatility induced stationarity;

    Sammanfattning : This thesis consists of four papers: Paper I is an overview of recent techniques in strong numerical solutions of stochastic differential equations, driven by Wiener processes, that have appeared the last then 10 years, or so. Paper II studies theoretical and numerical aspects of stochastic differential equations with so called volatility induced stationarity. LÄS MER

  7. 5. Variational Methods for Moments of Solutions to Stochastic Differential Equations

    Författare :Kristin Kirchner; Chalmers tekniska högskola; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Additive and multiplicative noise; Stochastic partial differential equation; Projective and injective tensor product space; Hilbert tensor product space; Space-time variational problem; Petrov-Galerkin discretization; Stochastic ordinary differential equation;

    Sammanfattning : Numerical methods for stochastic differential equations typically estimate moments of the solution from sampled paths. Instead, we pursue the approach proposed by A. Lang, S. Larsson, and Ch. LÄS MER