312.238 (20W) Stochastic Differential Equations

Wintersemester 2020/21

Registration deadline has expired.

First course session
13.10.2020 17:00 - 19:00 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
Type Lecture
Course model Attendance-based course
Hours per Week 2.0
ECTS credits 4.0
Registrations 7
Organisational unit
Language of instruction English
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

Lecture with practical examples
Combination of slides and tablet

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)

The final exam (which is announced as an oral exam) can be taken via BBB. For this, the possibility to write in front of the camera is required. The examiner must be able to watch the student as well as what is written at the same time.

Examination methodology

There will be a final exam, presumably at the end of January.
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.
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 final exam.

Grading scheme

Grade / Grade grading scheme

Position in the curriculum

  • Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
    • Subject: Applied Statistics (Compulsory elective)
      • 5.6 Stochastic Differential Equations ( 2.0h VO / 4.0 ECTS)
        • 312.238 Stochastic Differential Equations (2.0h VO / 4.0 ECTS)
  • Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
    • Subject: Applied Mathematics (Compulsory elective)
      • Lehrveranstaltungen aus den Vertiefungsfächern ( 0.0h XX / 12.0 ECTS)
        • 312.238 Stochastic Differential Equations (2.0h VO / 4.0 ECTS)

Equivalent courses for counting the examination attempts

Wintersemester 2023/24
  • 312.238 VO Stochastic Differential Equations (2.0h / 4.0ECTS)