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| Detailed information |
| Original study plan |
Bachelor's programme Technical Mathematics 2025W |
| Learning Outcomes |
Competences |
| Students are acquainted with the fundamental principles of stochastic simulation and the key algorithmical techniques required for computationally modelling and analysing stochastic processes.
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| Skills |
Knowledge |
- Simulate random numbers from a uniform distribution using techniques such as modular arithmetic and linear/mixed congruential generators.
* Assess the quality and performance of random number generators.
- Differentiate between random numbers and pseudo-random numbers.
- Simulate pseudo random numbers from various distributions using methods like the inverse transform method, rejection sampling, acceptance-rejection method, composition method, and ad-hoc methods.
- Simulate stochastic processes including random walks, Markov chains, Poisson processes, and Wiener processes and their extensions.
- Distinguish between exact simulation methods and numerical approximation methods for random variables and stochastic processes.
- Simulate simple stochastic differential equations (SDEs) ( learn/recall Ito's formula, simulate geometric Brownian motion, Wiener processes with drift, and the Ornstein-Uhlenbeck process).
- Apply numerical methods for solving SDEs, including the Euler-Maruyama method and the Milstein method.
- Compute the root mean square error (RMSE) to evaluate the simulations results.
- Conduct Monte Carlo simulations for various applications and implement variance reduction techniques (Analytical reduction, stratified sampling, importance sampling, use of covariates).
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Fundamental concepts of stochastic processes, techniques for random number generation, methods for simulating Markov chains and other stochastic models, Monte-Carlo simulation, practical applications of stochastic simulations in various fields, evaluation and interpretation of the results of stochastic simulations.
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| Criteria for evaluation |
Programming project in R and project presentation.
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| Methods |
Blackboard presentation, supported by lecture slides and software R
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| Language |
English and French |
| Study material |
- Random Number Generation and Monte Carlo Methods, J. E. Gentle
- Simulation, S. Ross,
- Simulation and Inference for Stochastic Differential Equations With R Examples, S. M. Iacus
- Stochastik: Theorie und Anwendungen, D. Meintrup and S. Schäffler
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| Changing subject? |
No |
| Earlier variants |
They also cover the requirements of the curriculum (from - to)
201WTMSSTSV20: VO Stochastic simulation (2020W-2022S)
TMCPAVOSIMU: VO Stochastic simulation (2004S-2020S)
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