Sökning: "stochastic heat equation"
Visar resultat 1 - 5 av 12 avhandlingar innehållade orden stochastic heat equation.
1. Approximating Stochastic Partial Differential Equations with Finite Elements: Computation and Analysis
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
2. Topics in Simulation and Stochastic Analysis
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
3. A weak space-time formulation for the linear stochastic heat equation
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
4. On weak and strong convergence of numerical approximations of stochastic partial differential equations
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. Selected Topics in Mathematical Modelling: Machine Learning and Tugs-of-War
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