MAGIC089: Stochastic Processes

Details Description Lecturer Bibliography Assessment Files Lectures

Course details

A core MAGIC course

Semester

Spring 2021: Monday, January 25th to Friday, March 19th; Monday, April 26th to Friday, May 7th

Hours

Live lecture hours: 10

Recorded lecture hours: 0

Total advised study hours: 40

Timetable

Thursdays: 10:05 - 10:55 (UK)

Description

The course will introduce the basic concept of stochastic processes.

As special and important example the Brownian motion is considered.

The general theory for semi-martingales is studied. The stochastic integral is introduced and the Ito formula derived.

Prerequisites

Measure theory and integration.

Basics of measure theoretical probability, for example in the sense of the first 5 chapters in Leo Breiman's book

Probability.

Syllabus

Introduction to general theory of stochastic processes
Construction of Brownian motion
General theory of stochastic processes
Stochastic Integration
Ito calculus

Lecturer

TK

Dr Tobias Kuna

University

University of Reading

Bibliography

Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.

Brownian motion (M{"o}rters and Peres, )
Stochastic integration with jumps (Bichtler, Klaus, )
Stochastic Integrations (von Weizsaecker, Heinrich and Winker, Gerhard, book)
Foundations of Modern Probability (Kallenberg, Olav, )
Probability (Breiman, )
Probability essentials (Jacod and Protter, )
Stochastic processes (Doob, )
Probability theory (Klenke, )
Measure Theory (Halmos, )

Assessment

The assessment for this course will be released on Monday 10th May 2021 at 00:00 and is due in before Tuesday 25th May 2021 at 11:00.

Results stated in the questions can be used in the later parts of the same question and the exam. Results from the lecture can be used when not requested otherwise. They need to be cited.

Full marks for this sheet corresponds to 50 marks. You can answer all the question (260 marks possible) and all marks achieved will be added. The final result will be capped at 100 marks.

Please note that you are not registered for assessment on this course.

Files

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Lectures

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