Stochastic Simulation of Processes, Fields and Structures
Dr. Tim Brereton
Time and Place
Monday, 8-10 am (220, Helmholtzstr. 18)
Tuesday, 10 am - noon (220, Helmholtzstr. 18)
Wednesday, 4-6 pm (120, Helmholtzstr. 18)
4 hours lecture and 2 hours excercise
Credit points: 9
Basic knowledge of probability calculus and statistics as taught, for example, in "Elementare Wahrscheinlichkeitsrechnung und Statistik".
Master students in "Mathematik", "Wirtschaftsmathematik" and "Mathematische Biometrie"
Master students from other fields (in particular Physics, Computer Science or Chemistry) are welcome as well; the respective examination board (Prüfungsausschuss) decides on the possible recognition of examinations.
In this course, we introduce a number of important stochastic models.
These include fundamental stochastic processes, such as Brownian motion, Gaussian processes and the Poisson process; important random field models and random graph models, including the Ising model and Gaussian random fields; and spatial point process models.
We will define these objects and consider a number of key properties. We will also consider a number of important problems relating to these objects. These problems come from finance, physics, operations research and biology.
We will focus on computational modeling of these objects. In particular, we will focus on efficiently simulating them. In doing so, we will discuss a number of recent developments in Monte Carlo methods, such as multilevel Monte Carlo and smart importance sampling.
This course is a great way to learn about lots of exciting applications of stochastic modeling, and to learn how to solve lots of interesting problems via simulation.
Requirements and Exam
In order to participate in the final exam, it is necessary to earn 50% of the points on all problem sheets. Students who want to do so are kindly asked to register for the 'Vorleistung' in the LSF-'Hochschulportal'.
Time and place
Wednesday, August 6 from 10 am to noon,
room 120 (Helmholtzstr. 18)
Wednesday, October 1 from 10 am to noon,
room 120 (Helmholtzstr. 18)
You will be allowed to bring a one-sided (!) handwritten A4 sheet with useful results from the lectures and exercises to the exam. Calculators are not permitted (you won't need one).
The exams are corrected!
You can find the number of points you obtained in the SLC as an extra exercise sheet (marked as "Prüfungsleistung"). The associated marks are indicated in the following tabular, it's the same for the first and second exam:
|1,0||42,5 - 50|
|1,3||40,5 - 42|
|1,7||38,5 - 40|
|2,0||36,5 - 38|
|2,3||34,5 - 36|
|2,7||33 - 34|
|3,0||31 - 32,5|
|3,3||29 - 30,5|
|3,7||27 - 28,5|
|4,0||25 - 26,5|
|5,0||0 - 24,5|
The post-exam review for the second exam will take place on Monday, October 6 from 2 to 3 pm in Lisa's office (room 1.42 in Helmholtzstr. 18).
Problem Sheet 01 Matlab Solution 01
Problem Sheet 02 Matlab Solution 02
Problem Sheet 03 Matlab Solution 03
Problem Sheet 04 Matlab Solution 04
Problem Sheet 05 Matlab Solution 05 Solution to Exercise 3
Problem Sheet 06 Matlab Solution 06
Problem Sheet 07 Matlab Solution 07
Problem Sheet 08 Matlab Solution 08
Problem Sheet 09 Matlab Solution 09
Problem Sheet 10 Matlab Solution 10
Problem Sheet 11 Matlab Solution 11
Problem Sheet 12 Matlab Solution 12 (you'll need the files below)
Files for Ex. 4: AllFiles.rar OR List of single files
In order to receive points for your problem sheets, a registration at SLC is required.
Lecture notes will usually be provided roughly two weeks after the correpsonding lectures.
Code From Recent Lectures (Not Yet in Lecture Notes)
Asmussen, S. and P. Glynn. Stochastic Simulation. Springer, 2007.
Brémaud, P. Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues. Springer, 1999.
Cont, R. and P. Tankov. Financial Modeling with Jump Processes. Chapman & Hall/CRC, 2003.
Glasserman, P. Monte Carlo Methods in Financial Engineering. Springer, 2004.
Graham, C. and D. Talay. Stochastic Simulation and Monte Carlo Methods: Mathematical Foundations of Stochastic Simulation. Springer, 2013.
Kroese, D. P., T. Taimre and Z. Botev. Handbook of Monte Carlo Methods. Wiley, 2011.
Møller, J. and Waagepetersen, R. P. Statistical Inference and Simulation for Spatial Point Processes. Chapman & Hall/CRC, 2003.
Ross, S. M. Simulation, Fifth Edition. Academic Press, 2012.
Winkler, G. Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction. Springer, 2003.
The SECOND exam is corrected! You can see the points you obtained in your SLC account, a tabular with the corresponding marks is on this page (section "Requirements and Exam").
Lecture notes updated again.
Note that the section in the lecture notes on SDEs is not yet finished. It will be updated as soon as possible. In the mean time, refer to your notes.
Lecture notes have been updated.
On this page you can send us anonymous comments on the lectures and exercise lessons.