Sökning: "Stochastic partial differential equations"

Visar resultat 1 - 5 av 33 avhandlingar innehållade orden Stochastic partial differential equations.

  1. 1. Exponential integrators for stochastic partial differential equations

    Författare :Rikard Anton; David Cohen; Christian Engström; Stig Larsson; Annika Lang; Umeå universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Stochastic partial differential equations; numerical methods; stochastic exponential integrator; strong convergence; trace formulas;

    Sammanfattning : Stochastic partial differential equations (SPDEs) have during the past decades become an important tool for modeling systems which are influenced by randomness. Because of the complex nature of SPDEs, knowledge of efficient numerical methods with good convergence and geometric properties is of considerable importance. 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. 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

  5. 4. Numerical Complexity Analysis of Weak Approximation of Stochastic Differential Equations

    Författare :Raul Tempone Olariaga; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Adaptive methods; a posteriori error estimates; stochastic differential equations; weak approximation; Monte Carlo methods; Malliavin Calculus; HJM model; option price; bond market; stochastic elliptic equation; Karhunen-Loeve expansion; numerical co; Numerical analysis; Numerisk analys;

    Sammanfattning : The thesis consists of four papers on numerical complexityanalysis of weak approximation of ordinary and partialstochastic differential equations, including illustrativenumerical examples. Here by numerical complexity we mean thecomputational work needed by a numerical method to solve aproblem with a given accuracy. LÄS MER

  7. 5. The Skorohod problem and weak approximation of stochastic differential equations in time-dependent domains

    Författare :Thomas Önskog; Kaj Nyström; Leif Persson; Johan Tysk; Umeå universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Skorohod problem; weak approximation; time-dependent domain; stochastic differential equations; parabolic partial differential equations; oblique reflection; stopped diffusions; Euler scheme; adaptive methods; sensitivity analysis; financial derivatives; Greeks ; MATHEMATICS; MATEMATIK; Mathematics; matematik;

    Sammanfattning : This thesis consists of a summary and four scientific articles. All four articles consider various aspects of stochastic differential equations and the purpose of the summary is to provide an introduction to this subject and to supply the notions required in order to fully understand the articles. LÄS MER