Skip to main content

LUP Student Papers

LUND UNIVERSITY LIBRARIES

STEP SIZE CONTROL FOR THE NUMERICAL APPROXIMATION OF STOCHASTIC DIFFERENTIAL EQUATIONS

Schumacher, Claas LU (2024) In Master's Theses in Mathematical Sciences NUMM03 20231
Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
Abstract
This thesis investigates the effectiveness of step size control in the numerical
simulation of Stochastic Differential Equations (SDEs). The study is divided into
a theoretical exploration and a series of numerical experiments. The theoretical
section introduces key definitions and theorems, delves into the properties of
Brownian motion, and examines the conditions under which solutions to SDEs
can be found. The Euler-Maruyama method’s convergence rate is also determined.
In the experimental section, the thesis applies a step size control strategy to
the Euler-Maruyama method and a Runge-Kutta method. Through simulations
of the stochastic Van der Pol oscillator and the Black-Scholes equation, it is
demonstrated that step size... (More)
This thesis investigates the effectiveness of step size control in the numerical
simulation of Stochastic Differential Equations (SDEs). The study is divided into
a theoretical exploration and a series of numerical experiments. The theoretical
section introduces key definitions and theorems, delves into the properties of
Brownian motion, and examines the conditions under which solutions to SDEs
can be found. The Euler-Maruyama method’s convergence rate is also determined.
In the experimental section, the thesis applies a step size control strategy to
the Euler-Maruyama method and a Runge-Kutta method. Through simulations
of the stochastic Van der Pol oscillator and the Black-Scholes equation, it is
demonstrated that step size control can enhance simulation results, although the
choice of parameters is critical to its success. (Less)
Please use this url to cite or link to this publication:
author
Schumacher, Claas LU
supervisor
organization
alternative title
Steglängkontroll för numerisk approximation av stokastiska differentialekvationer
course
NUMM03 20231
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Master's Theses in Mathematical Sciences
report number
LUNFNA-3042-2024
ISSN
1404-6342
other publication id
2024:E51
language
English
id
9169324
date added to LUP
2024-10-29 17:14:24
date last changed
2024-10-29 17:14:24
@misc{9169324,
  abstract     = {{This thesis investigates the effectiveness of step size control in the numerical
simulation of Stochastic Differential Equations (SDEs). The study is divided into
a theoretical exploration and a series of numerical experiments. The theoretical
section introduces key definitions and theorems, delves into the properties of
Brownian motion, and examines the conditions under which solutions to SDEs
can be found. The Euler-Maruyama method’s convergence rate is also determined.
In the experimental section, the thesis applies a step size control strategy to
the Euler-Maruyama method and a Runge-Kutta method. Through simulations
of the stochastic Van der Pol oscillator and the Black-Scholes equation, it is
demonstrated that step size control can enhance simulation results, although the
choice of parameters is critical to its success.}},
  author       = {{Schumacher, Claas}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{STEP SIZE CONTROL FOR THE NUMERICAL APPROXIMATION OF STOCHASTIC DIFFERENTIAL EQUATIONS}},
  year         = {{2024}},
}