# 2D1269, Matematiska modeller, analys och simulering, del 2, 5 poäng

## Mathematical Models, Analysis and Simulation, Part II:

## Numerical Methods for Stochastic Differential Equations

- Starts January 2006,
- The course is not given 2004/2005,
- The teaching of 2D5218 and 2D5227 (graduate course),
2D1269 (undergraduate) coincides.

The course is organized by the
department of Numerical Analysis and Computing Science (NADA). It is
open for both graduate and undergraduate students
and can be taken indepently from part I, with the same
prerequisites.

The goal of this course is to give basic knowledge of applied and
numerical mathematics useful for scientific and engineering modelling,
guided by some problems in applications.

This year the course treat stochastic differential equations
and their numerical solution, with applications in
financial mathematics, material science, geophysical flow problems, turbulent diffusion,
control theory and Monte Carlo methods.

We will discuss basic questions
for solving stochastic differntial equations,
e.g.
to determine the price of an option
is it more efficient to solve the deterministic
Black and Scholes partial differential equation or
use a Monte Carlo method based on stochastics?

The course treats basic theory of stochastic differential equations
including weak and strong approximation,
efficient numerical methods and error estimates,
the relation between stochastic
differential equations and partial differential equations,
stochastic partial differential equations, variance reduction.

The text for the course is the NADA-lecture notes

*Stochastic and Partial Differential Equations with Adapted Numerics*,
authored by the teachers

The prerequisite
for the course is knowledge of basic courses in mathematics and
numerical analysis at a Swedish university, or the equivalent.
* Part II can be studied separately from Part I*.
Some
experience of computer programming and the use of UNIX systems or
personal computers is assumed. The homework and computer laboratories
constitute a very important part of the course. Computer lab's will be
done in MATLAB with existing software for the student to modify and
experiment with.

Course administrator: Anders Szepessy.

Formal description,
that is, the text in the studiehandbook.

Up to *Nada courses*.

Responsible for this page: <szepessy@nada.kth.se>

Latest change May 31, 2005

Technical support: <webmaster@nada.kth.se>