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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 Federico Ciech
Federico Ciech
(Sussex)
Photo of Raffaele Grande
Raffaele Grande
(Cardiff)
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 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:

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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.

Assignment Stochastic Process 2017

Files:Exam paper
Released: Monday 24 April 2017 (63.4 days ago)
Deadline: Sunday 7 May 2017 (49.4 days ago)
Instructions:

Results stated in the questions can be used in the later parts of the same question.
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
1-2SPLectNAI.pdfL
3-6SPLectNA_part_2.pdfL
6-10SPLectNA_part_3.pdfL
6SPLectNA_part_4.pdfL
10SPLectNA_Erratum.pdfL
10-0SP_Magic_solutions.pdfL


Recorded Lectures


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