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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 2017 (Monday, January 23 to Friday, March 31)

Timetable

  • Fri 10:05 - 10:55

Prerequisites

Measure theory and integration. Basics of measure theoretical probability.

Syllabus

• Construction of Brownian motion • Path properties • Transformation invariances of Brownian Motion • Path properties of Brownian motion • Tail events and zero-one laws • Stochastic Integration • Ito calculus • Asymptotic properties of processes: the law of iterated logarithm

Lecturer


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


Students


Photo of Jack Aiston
Jack Aiston
(Newcastle)
Photo of Marco Baffetti
Marco Baffetti
(Nottingham)
Photo of Seb Chan
Seb Chan
(Reading)
Photo of Junbin Chen
Junbin Chen
(Durham)
Photo of Raffaele Grande
Raffaele Grande
(Cardiff)
Photo of Xin Guo
Xin Guo
(Liverpool)
Photo of Tanmay Inamdar
Tanmay Inamdar
(East Anglia)
Photo of Ewan Johnstone
Ewan Johnstone
(Liverpool)
Photo of Yuija Liu
Yuija Liu
(Loughborough)
Photo of Alexander Owen
Alexander Owen
(Exeter)
Photo of Filippo Pagani
Filippo Pagani
(Manchester)
Photo of Adam Peddle
Adam Peddle
(Exeter)
Photo of Norbert Pintye
Norbert Pintye
(Loughborough)
Photo of Luke Smallman
Luke Smallman
(Cardiff)
Photo of Chen Wang
Chen Wang
(Manchester)
Photo of Patrick WRIGHT
Patrick WRIGHT
(Leeds)


Bibliography


Brownian motionM{"o}rters and Peres
ProbabilityBreiman
Probability essentialsJacod and Protter
Time series: theory and methodsBrockwell and Davis
Stochastic processesDoob
Probability theoryKlenke


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



The course will be assessed by a single take-home exam paper in April which should be completed during a 2 weeks time and submitted via the Magic website.
You can answer all questions and 50 marks is the maximum you can achieve. The paper contains more than 50 marks and hence not all questions need to be answered to obtain full marks.
Submit your answer either handwritten and scanned or written in LaTex via the Magic website.
No assignments have been set for this course.

No assignments have been set for this course.

Files


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

Week(s)File
1-2SPLectNAI.pdfL
3-6SPLectNA_part_2.pdfL
6-10SPLectNA_part_3.pdfL
6SPLectNA_part_4.pdfL


Recorded Lectures


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