Sökning: "numerical approximation of stochastic differential equations"

Visar resultat 1 - 5 av 21 avhandlingar innehållade orden numerical approximation of stochastic differential equations.

  1. 1. 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

  3. 2. 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

  4. 3. 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

  5. 4. 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

  7. 5. 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