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Numerics of stochastic processes

Dates
Tu
10:00 am - noon
Lecture
MA749
Dr. Raphael Kruse
We
4:00 pm - 6:00 pm
Exercise class
(every second week)
MA648
tba
Th 
8:00 am - 10:00 am
Lecture
MA749
Dr. Raphael Kruse
Secretary
MA568
Alexandra Schulte

Description

This lecture surveys numerical methods for the approximation of stochastic differential equations. In particular, we study which properties of the exact solution determine the order of convergence and how methods of higher order are constructed. Further topics like efficient implementation are discussed as well through numerical experiments (written in Python).

Contents:

  • Wiener processes and Brownian motion
  • the stochastic Itô integral
  • stochastic differential equations (existence, uniqueness, regularity)
  • Convergence, stability, and consistency of numerical methods, in particular of the Euler-Maruyama method, Milstein method, and Itô-Taylor methods.
  • Strong versus weak convergence of numerical methods
  • (multilevel) Monte Carlo methods for stochastic differential equations

The lecture yields 10 ETCS.

Requirements

Strongly recommended:

  • Analysis III, Measure and integration theory, Probability I and II.
  • Knowledge of one programming language (like Python or Matlab)
  • Basic course on Numerics.

Recommended:

  • Numerics for ODE

Exams

Credit points will be awarded for passing the final oral exam. Further details will be announced in the lecture.

Literature

A list of reference will be provided on the accompanying course page on ISIS.

Zusatzinformationen / Extras

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