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General


This course is part of the MAGIC core.

Description

The course will introduce the basic concept of stochastic processes. As special and important example the Brownian motion is considered. The general theory of stochastic processes is studied. The stochastic integral is introduced and the Ito formula derived.

Semester

Spring 2020 (Monday, January 20 to Friday, March 27)

Hours

  • Live lecture hours: 10
  • Recorded lecture hours: 0
  • Total advised study hours: 40

Timetable

  • Thu 10:05 - 10:55

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

Other courses that you may be interested in:

Lecturer


Tobias Kuna
Email t.kuna@reading.ac.uk
Phone 01183786028
Photo of Tobias Kuna


Bibliography


Brownian motionM{"o}rters and Peres
Stochastic integration with jumpsBichtler, Klaus
Stochastic Integrationsvon Weizsaecker, Heinrich and Winker, Gerhard
Foundations of Modern ProbabilityKallenberg, Olav
ProbabilityBreiman
Probability essentialsJacod and Protter
Stochastic processesDoob
Probability theoryKlenke
Measure TheoryHalmos


Note:

Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will 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.)

Assessment



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 (100 marks possible) and all marks achieved will be added. The final result will be capped at 50 marks.

No assignments have been set for this course.

Recorded Lectures


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