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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 2018 (Monday, January 22 to Friday, March 16; Monday, April 23 to Friday, May 4)

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
Photo of Tobias Kuna


Students


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Bibliography


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


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