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Stochastic Simulation
Stochastische Simulation
Last Updated: 2026-02-05 15:13:59
Abstract
Examples of simulations in various fields of applications, basic algorithms for the generation of random variables, estimates for the precision of simulation results, variance reduction, introduction to Markov chain Monte Carlo.
Objective
Stochastic simulation (also called Monte Carlo method) is the experimental analysis of a stochastic model by implementing it on a computer. Probabilities and expected values can then be approximated by averaging, The central limit theorem gives an estimate of the error in this approximation. The course shows with examples the many uses of stochastic simulation and explains the different algorithms that are used. These algorithms are illustrated with the statistical software R.
Content
Examples of simulations in computer science, numerics, statistics, statistical mechanics, Operations research, financial mathematics and its uses as a teaching tool. Generation of uniform random variables, the period and the lattice structure of linear congruence generators. Generation of random variables with arbitrary distribution (quantile transform, accept-reject, importance sampling, ratio of uniforms etc.), simulation of Gaussian processes and diffusions. The precision of simulatios, methods for variance reduction. Introduction to Markov chains and Markov chain Monte Carlo (Metropolis-Hastings, Gibbs sampler, reversible jumps).
Resources
Lecture Notes
There is a script available, but at the moment only in German. The code for thedemonstration is available on my home page.
Literature
P. Glasserman, Monte Carlo Methods in Financial Engineering. Springer 2004. B. D. Ripley. Stochastic Simulation. Wiley, 1987. Ch. Robert, G. Casella. Monte Carlo Statistical Methods. Springer 2004 (2nd edition).
General Information
- Language
- German
- Levels
- BSC , MSC
- Frequency
- Every two years
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise |
Stochastische Simulation
by request in English
|
|
3 h weekly |