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250157 VO Stochastic Analysis (2021W)
Labels
MIXED
Registration/Deregistration
Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Details
Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
Wednesday
06.10.
17:15 - 18:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
07.10.
15:00 - 16:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
13.10.
17:15 - 18:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
14.10.
15:00 - 16:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
20.10.
17:15 - 18:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
21.10.
15:00 - 16:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
27.10.
17:15 - 18:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
28.10.
15:00 - 16:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
03.11.
17:15 - 18:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
04.11.
15:00 - 16:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
10.11.
17:15 - 18:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
11.11.
15:00 - 16:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
17.11.
17:15 - 18:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
18.11.
15:00 - 16:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
24.11.
17:15 - 18:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
25.11.
15:00 - 16:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
01.12.
17:15 - 18:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
02.12.
15:00 - 16:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
09.12.
15:00 - 16:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
15.12.
17:15 - 18:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
16.12.
15:00 - 16:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
12.01.
17:15 - 18:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
13.01.
15:00 - 16:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
19.01.
17:15 - 18:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
20.01.
15:00 - 16:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
26.01.
17:15 - 18:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
27.01.
15:00 - 16:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Information
Aims, contents and method of the course
This course aims at rigorously developing Ito's theory of stochastic calculus and presenting some of its fundamental applications.Some of the keywords are: Gaussian processes, Brownian motion, conditional expectation, martingales, stopping times, optional stopping, local martingales, stochastic integral, Ito's lemma.We will first construct Brownian motion and derive its basic properties. Then, we will develop a formal theory of continuous martingales and local martingales, on which we will build the stochastic integral.Towards the end of the course we will use the constructed theory of stochastic calculus to derive some deep results on the nature of Brownian motion (like for example conformal invariance of two-dimensional Brownian motion).Familiarity with Advanced Probability will be assumed. However, we will recall the notion of conditional expectation. Elements of complex analysis will be used towards the end of the course.
Assessment and permitted materials
Oral exam at the end of the course.
Minimum requirements and assessment criteria
Examination topics
Reading list
We will loosely follow (the first 4 chapters of) the lecture notes of Nathanael Berestycki:https://homepage.univie.ac.at/nathanael.berestycki/teach/StoCal/sc3.pdfAnother valuable source is the bookBrownian Motion, Martingales, and Stochastic Calculus by J-F. Le Gall
Association in the course directory
MSTV
Last modified: We 18.01.2023 00:26