MAGIC065: Stochastic Processes

Course details

A core MAGIC course

Semester

Autumn 2010
Monday, October 4th to Friday, December 17th

Hours

Live lecture hours
20
Recorded lecture hours
0
Total advised study hours
0

Timetable

Mondays
12:05 - 12:55
Fridays
10:05 - 10:55

Description

Prerequisites

No prerequisites information is available yet.

Syllabus

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Part I (Voss, Lythe and Molina-Paris)
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1-1 Discrete random variables. Continuous random variables. Independence.
1-2 Random walk. Binomial distribution, Poisson distribution.
1-3 Gambler's ruin. Occupation and exit time. First-step analysis.
1-4 Markov Chains. Birth and death processes. Gillespie algorithm.
1-5 Chapman-Kolmogorov equation (To glue to Markov chains?)
1-6 Stationary distributions, quasi-limiting distributions.
1-7 Stochastic processes. Wiener process. Diffusion equation.
1-8 The reflection principle and passage times. Conditional hitting probability.
1-9 Ornstein-Uhlenbeck processes. Bessel processes.
1-10 Numerical methods.
1-11 Applications to biology.
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Part II (Veretennikov) Syllabus
======================
2-1 Stochastic processes; some measure theory; Kolmogorov continuity theorem.
2-2 Filtrations and conditional expectations.
2-3 Wiener measure.
2-4 Stochastic Ito integrals.
2-5 Stopping times; martingales; Kolmogorov and Doob theorems.
2-6 Ito formula.
2-7 Stochastic differential equations, existence and uniqueness of solutions.
2-8 Passage times, links to Laplace and Poisson equations;Dynkin and Feynman-Kac formulae.
2-9 Girsanov change of measure; weak solutions of SDEs.
2-10 Dependence of solutions of SDEs from initial data; Markov property of solutions.

Lecturers

  • AV

    Professor Alexander Veretennikov

    University
    University of Leeds
    Role
    Main contact
  • GL

    Dr Grant Lythe

    University
    University of Leeds
  • CM

    Dr Carmen Molina-Paris

    University
    University of Leeds
  • JV

    Dr Jochen Voss

    University
    University of Leeds

Bibliography

Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and 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.

  • Introduction to the Theory of Random Processes (Krylov, book)
  • Stochastic Calculus and Financial Applications (J Michael Steele, book)
  • An Introduction to Stochastic Modelling (Taylor and Karlin, book)

Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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