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TU Dortmund Lehrstuhl für Stochastik und Analysis

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Adresse (Briefe):

Technische Universität Dortmund
Fak. Mathematik, LS IV
44221 Dortmund

Adresse (Lieferungen):

Technische Universität Dortmund
Fak. Mathematik, LS IV
Vogelpothsweg 87
44227 Dortmund


Telefonnummern und Email-Adressen:

Fr. I. Rzepka (Sekretariat):
(+49) 231 / 755-3062

Fax: (+49) 231 / 755-3064


Links


Selected topics in stochastic analysis

News

12.07.2017
Starting today, Mrs. Rzepka has a list for you to sign up for the exam. The possible dates are:
  • 02.08.2017, 10:00-12:00, room M/612
  • 20.09.2017, 10:00-12:00, room M/612
10.05.2017
  • Exercise sheet 2 is available online
  • Starting next Wednesday (17.05.2017), every other Wednesday our class will meet in room 919
08.05.2017
Starting today, we switch the topic to the Stein method.
26.04.2017
The exercise 4 part ii) of Exercise Sheet 1 is postponed until the next Exercise session.
19.04.2017:
The department website had an error in the date of the first meeting of the course. Because of this in the first class we reviewed some properties of Brownian motion and slowly introduced the Wiener integral and discussed some of it's properties.
19.04.2017:
This website is created.

Exercise Sheets

Schedule

The lectures and exercise sessions take place on Mondays 13-15 and Wednesdays 10-12 in room M 611. The exercise sessions will always take place on Wednesdays, for the precise schedule see the table below keeping in mind that it is subject to change. All changes to the schedule will be announced in class and on this websita. The first lecture is on Wednesday 19.04.2017.

date type topics/notes
04-17 Mon NO CLASS Ostermontag
04-19 Wed LECTURE Brownian motion, Wiener integral
04-24 Mon LECTURE Wiener-Itô chaos decomposition of the L² space, multiple Wiener-Itô integrals
04-26 Wed LECTURE multiple Wiener-Itô integrals, tensor products and contractions
05-01 Mon NO CLASS Maifeiertag
05-03 Wed EXERCISE Exercise Sheet 1
Problem 4 ii) postponed until next Exercise session
Wiener-Itô chaos decomposition for L² random variables
05-08 Mon LECTURE Distance between probability measures
05-10 Wed LECTURE Convergence in distribution
05-15 Mon LECTURE Introduction to Stein's method
05-17 Wed EXERCISE Exercise Sheet 2
05-22 Mon LECTURE Introduction to Stein's method
05-24 Wed EXERCISE Exercise Sheet 3
05-29 Mon NO CLASS due to sickness
05-31 Wed EXERCISE Exercise Sheet 4
06-05 Mon NO CLASS Pfingstmontag
06-07 Wed LECTURE Malliavin derivative
06-12 Mon LECTURE Malliavin derivative in the L²(T,B,μ) case
06-14 Wed LECTURE Divergence operator and Skorokhod integral
06-19 Mon LECTURE Berry–Esseen theorem
06-21 Wed EXERCISE Exercise Sheet 5
06-26 Mon LECTURE Stochastic integration with respect to Gaussian Volterra processes
06-28 Wed LECTURE Berry-Esseen theorem
07-03 Mon LECTURE Berry-Esseen theorem
07-05 Wed EXERCISE
07-10 Mon LECTURE The Itô integral
07-12 Wed LECTURE The Itô formula
07-17 Mon LECTURE
07-19 Wed EXERCISE
07-24 Mon LECTURE
07-26 Wed EXERCISE

Info

In case of questions, contact Dr. Benedykt Szozda or Dr. Raghid Zeineddine, or visit us in our office M 612.

Grading

The final grade will be based on an oral exam. In order to attend the examination, students have to participate in the exercise sessions presenting solutions to some of the problems from the exercise sheets.