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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


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Assessment



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Recorded Lectures


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