312.239 (20W) Stochastic Differential Equations, exercises

Wintersemester 2020/21

Registration deadline has expired.

First course session
13.10.2020 16:00 - 17:00 N.0.07 On Campus
... no further dates known

Overview

Due to the COVID-19 pandemic, it may be necessary to make changes to courses and examinations at short notice (e.g. cancellation of attendance-based courses and switching to online examinations).

For further information regarding teaching on campus, please visit: https://www.aau.at/en/corona.
Lecturer
Course title german Stochastic Differential Equations, exercises
Type Practical class (continuous assessment course )
Course model Attendance-based course
Hours per Week 1.0
ECTS credits 2.0
Registrations 6 (25 max.)
Organisational unit
Language of instruction Englisch
Course begins on 13.10.2020
eLearning Go to Moodle course

Time and place

Please note that the currently displayed dates may be subject to change due to COVID-19 measures.
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Course Information

Intended learning outcomes

Understanding the theoretical basis needed for the construction of stochastic integrals and for the study of stochastic differential equations (martingales in continuous time, stochastic integrals, Itô's formula)

Knowledge on stochastic differential equations (strong and weak solutions, existence and uniqueness of solutions)

Ability to solve a given stochastic differential equation (explicit solutions, numerical methods)

Teaching methodology

Take home exercises and in-class presentations by the students

Course content

Theoretical basis:
Martingales in continuous time
Stochastic integrals
Itô's formula

Stochastic differential equations:
Strong and weak solutions
Existence and uniqueness of solutions
Explicit solutions
Numerical methods

Prior knowledge expected

Stochastics 2
Stochastic processes

Literature

Bernt Oksendal: Stochastic Differential Equations, Springer, 2010.

Examination information

Im Fall von online durchgeführten Prüfungen sind die Standards zu beachten, die die technischen Geräte der Studierenden erfüllen müssen, um an diesen Prüfungen teilnehmen zu können.

Modified examination information (exceptional COVID-19 provisions)

In case of a lookdown the exercise class will be continued via BigBlueButton on moodle. The exercise sheets then have to be handed in online in moodle until 13 o'clock at the day of the exercise class and the presentations on the board will be supplemented by presentations in BigBlueButton.

Examination methodology

There are 100 p. in total. The number of exercises solved counts 80 p., the presentation in total counts 20 p. There will be weekly exercise sheets that need to be solved. In the exercise class students will tick all the exercises they solved and hand in the solutions. Out of these solutions a random sample will be checked every week in order to make sure that all ticks were correct. For the solved exercises the students get points, which will add up to 80 for all exercises. In class the students have to present some of the exercises. For the quality of the presentations they get an average grade over the whole semester of at most 20 p.

The point scheme is as follows:
100-87 p. -> 1
86-75 p. -> 2
74-62 p. -> 3
61-50 p. -> 4
49-0 p. -> 5

Examination topic(s)

Everything that is covered in the lecture and hence also in the exercise class.
If additional reading is required for the lecture, this will be clearly announced in the lecture.

Assessment criteria / Standards of assessment for examinations

The mark depends only on the number of points the student achieves at the exercises.

Sign-out without grading is possible until October 31, 2020.

Grading scheme

Grade / Grade grading scheme

Position in the curriculum

  • Master's degree programme Mathematics (SKZ: 401, Version: 18W.1)
    • Subject: Applied Statistics (Compulsory elective)
      • 5.6 Stochastic Differential Equations ( 1.0h UE / 2.0 ECTS)
        • 312.239 Stochastic Differential Equations, exercises (1.0h UE / 2.0 ECTS)
  • Master's degree programme Mathematics (SKZ: 401, Version: 18W.1)
    • Subject: Applied Mathematics (Compulsory elective)
      • Lehrveranstaltungen aus den Vertiefungsfächern ( 0.0h XX / 12.0 ECTS)
        • 312.239 Stochastic Differential Equations, exercises (1.0h UE / 2.0 ECTS)

Equivalent courses for counting the examination attempts

Wintersemester 2023/24
  • 312.239 UE Stochastic Differential Equations, exercises (1.0h / 2.0ECTS)