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Stochastic Simulation
Last Updated: 2026-02-05 15:35:17
Abstract
This course introduces statistical Monte Carlo methods. This includes applications of stochastic simulation in various fields (statistics, statistical mechanics, operations research, financial mathematics), generating uniform and arbitrary random variables (incl. rejection and importance sampling), the accuracy of methods, variance reduction, quasi-Monte Carlo, and Markov chain Monte Carlo.
Objective
Students know the stochastic simulation methods introduced in this course. Students understand and can explain these methods, show how they are related to each other, know their weaknesses and strengths, apply them in practice, and proof key results.
Content
Examples of simulations in different fields (statistics, statistical mechanics, operations research, financial mathematics). Generation of uniform random variables. Generation of random variables with arbitrary distributions (including rejection sampling and importance sampling), simulation of multivariate normal variables and stochastic differential equations. The accuracy of Monte Carlo methods. Methods for variance reduction and quasi-Monte Carlo. Introduction to Markov chains and Markov chain Monte Carlo (Metropolis-Hastings, Gibbs sampler, Hamiltonian Monte Carlo, reversible jump MCMC). Algorithms introduced in the course are illustrated with the statistical software R.
Resources
Lecture Notes
A script will be available in English.
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
- English
- Levels
- MSC , WBZ
- Frequency
- Every two years
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise |
Stochastic Simulation
The lecturers will communicate the exact lesson times of ONLINE courses.
|
|
3 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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Statistics Master (The following courses belong to the curriculum of the Master's Programme in Statistics. The corresponding credits do not count as external credits even for course units where an enrolment at ETH Zurich is not possible.)
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