Lecturer
Dr. Tim Brereton

Teaching assistant
Lisa Handl

Time and Place

Lecture
Monday, 8-10 am (220, Helmholtzstr. 18)
Tuesday, 10 am - noon (220, Helmholtzstr. 18)

Excercise session
Wednesday, 4-6 pm (120, Helmholtzstr. 18)

Type

4 hours lecture and 2 hours excercise

Credit points: 9

Prerequisites

Basic knowledge of probability calculus and statistics as taught, for example, in "Elementare Wahrscheinlichkeitsrechnung und Statistik".

Intended Audience

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.

Contents

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

First exam:

Wednesday, August 6 from 10 am to noon,
room 120 (Helmholtzstr. 18)

Second exam:

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:

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 Sheets

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

Lecture notes will usually be provided roughly two weeks after the correpsonding lectures. 

Lecture notes

Code From Recent Lectures (Not Yet in Lecture Notes)

Birth and death process

Finite state space Markov chain

Literature

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.