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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. Different constructions for Brownian motion are given and the main properties of Brownian motion are derived and proven. The stochastic integral is introduced and the Ito formula derived.

Semester

Spring 2019 (Monday, January 21 to Friday, March 29)

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.

Syllabus

  • Introduction to general theory of stochastic processes
  • Construction of Brownian motion
  • Transformation invariances of Brownian Motion
  • Path properties of Brownian motion
  • Stochastic Integration
  • Ito calculus
  • One example of a stochastic differential equation

Lecturer


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


Bibliography


Brownian motionM{"o}rters and Peres
ProbabilityBreiman
Probability essentialsJacod and Protter
Stochastic processesDoob
Probability theoryKlenke
Measure TheoryHalmos


Note:

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Assessment



The assessment will be given by a take home exam during the exam period. The exam sheet will contain more marks than necessary to obtain the full mark for the assignment. Details will be given on the assignment sheet itself.

Stochastic Process Exam

Files:Exam paper
Released: Sunday 28 April 2019 (54.0 days ago)
Deadline: Wednesday 15 May 2019 (36.0 days ago)
Instructions:

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.



Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
1-2SPLectNA_1_201819.pdf
3-4SPLectNA_2_201819.pdf
5-7SPLectNA_3_201819.pdf
8-10SPLectNA_4_201819.pdf
11SP_Magic_Exercise_Solutions.pdf


Recorded Lectures


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