Sökning: "stochastic calculus"
Visar resultat 1 - 5 av 20 avhandlingar innehållade orden stochastic calculus.
1. Some Extensions of Fractional Ornstein-Uhlenbeck Model : Arbitrage and Other Applications
Sammanfattning : This doctoral thesis endeavors to extend probability and statistical models using stochastic differential equations. The described models capture essential features from data that are not explained by classical diffusion models driven by Brownian motion.New results obtained by the author are presented in five articles. LÄS MER
2. Numerical Complexity Analysis of Weak Approximation of Stochastic Differential Equations
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. On weak convergence, Malliavin calculus and Kolmogorov equations in infinite dimensions
Sammanfattning : This thesis is focused around weak convergence analysis of approximations of stochastic evolution equations in Hilbert space. This is a class of problems, which is sufficiently challenging to motivate new theoretical developments in stochastic analysis. LÄS MER
4. The Finite Element Method for Fractional Order Viscoelasticity and the Stochastic Wave Equation
Sammanfattning : This thesis can be considered as two parts. In the first part a hyperbolic type integro-differential equation with weakly singular kernel is considered, which is a model for dynamic fractional order viscoelasticity. In the second part, the finite element approximation of the linear stochastic wave equation is studied. LÄS MER
5. Barycentric Markov processes and stability of stochastic integrators
Sammanfattning : This thesis consists of four papers that broadly concerns two dierent topics. The rsttopic is so-called barycentric Markov processes. By a barycentric Markov process wemean a process that consists of a point/particle system evolving in (discrete) time,whose evolution depends in some way on the mean value of the current points in thesystem. LÄS MER