Search for dissertations about: "Lévy process"

Showing result 6 - 10 of 26 swedish dissertations containing the words Lévy process.

  2. 6. Approximating Stochastic Partial Differential Equations with Finite Elements: Computation and Analysis

    Author : Andreas Petersson; Chalmers tekniska högskola; []
    Keywords : 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;

    Abstract : 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. READ MORE

  4. 7. Nelson-type Limits for α-Stable Lévy Processes

    Author : Haidar Al-Talibi; Astrid Hilbert; Francesco Russo; Linnéuniversitetet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Ornstein-Uhlenbeck position process; α-stable Lévy noise; scaling limits; time change; stochastic Newton equations; Mathematical statistics; Matematisk statistik; Applied mathematics; Tillämpad matematik; Mathematics; Matematik;

    Abstract : Brownian motion has met growing interest in mathematics, physics and particularly in finance since it was introduced in the beginning of the twentieth century. Stochastic processes generalizing Brownian motion have influenced many research fields theoretically and practically. READ MORE

  5. 8. Derivative Prices for Models using Levy Processes and Markov Switching

    Author : Sebastian Rasmus; Matematisk statistik; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; programming; operations research; Statistics; Regime switching; Levy processes; Derivative pricing; Computer simulations; actuarial mathematics; Statistik; operationsanalys; programmering; aktuariematematik;

    Abstract : This thesis contributes to mathematics, finance and computer simulations. In terms of mathematics this thesis concerns applied probability and Lévy processes and from the financial point of view the thesis concerns derivative pricing. Within these two areas several simulation techniques are investigated. The thesis is organized as follows. READ MORE

  6. 9. Approximation of Infinitely Divisible Random Variables with Application to the Simulation of Stochastic Processes

    Author : Magnus Wiktorsson; Matematisk statistik; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; operations research; Statistics; aktuariematematik; Stochastic differential equation; Infinitely divisible distribution; Type G distribution; Lévy process; Stochastic integral; Mathematical Statistics; Matematik; Mathematics; programming; actuarial mathematics; Statistik; operationsanalys; programmering;

    Abstract : This thesis consists of four papers A, B, C and D. Paper A and B treats the simulation of stochastic differential equations (SDEs). The research presented therein was triggered by the fact that there were not any efficient implementations of the higher order methods for simulating SDEs. READ MORE

  7. 10. Contributions to Numerical Solution of Stochastic Differential Equations

    Author : Anders Muszta; Göteborgs universitet; []
    Keywords : 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;

    Abstract : 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. READ MORE