MAGIC047: Introduction to Markov processes and Poisson equations

Course details

A specialist MAGIC course

Semester

Autumn 2008
Monday, October 6th to Friday, December 12th

Hours

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

Timetable

Tuesdays
09:05 - 09:55
Thursdays
11:05 - 11:55

Announcements

The last file has been corrected.
AYV

Description

Provisional syllabus:
  1. General notions of stochastic processes and integration, including conditional expectations. Lectures 1-4.
  2. Markov chains (MCs). Classical ergodic theorem with Kolmogorov's and Doeblin's proofs. Lectures 5-6.
  3. Non-uniformly ergodic MCs, recurrence. Lectures 7-8.
  4. Limit theorems for Markov chains: Law of Large Numbers (LLN) and Central Limit Theorem (CLT). Revision of Fourier analysis required for LLN and CLT. Lectures 9-11.
  5. Poisson equations in the whole space. Solutions via resolvents. Lectures 12-13.
  6. Poisson equations in the whole space depending on parameters. Smoothness of solutions. Invariant measures depending on parameters and their smoothness. Lectures 14-16.
  7. Some applications to stochastic algorithms. Lectures 17-20.

Provisional recommended books:
  1. Stirzaker, D. Stochastic processes and models. Oxford University Press, Oxford, 2005.
  2. Schinazi, R.B. Classical and spatial stochastic processes. Birkhauser Boston, Boston, MA, 1999.
  3. Benveniste, A., Metivier, M., Priouret, P. Adaptive algorithms and stochastic approximations. Springer-Verlag, Berlin, 1990.
  4. Ethier, S.N., Kurtz, T.G. Markov processes. Characterization and convergence. John Wiley and Sons, Inc., New York, 1986.

Prerequisites

UG Introduction to Probability, Statistical Methods, and Markov Processes courses. Some knowledge of Lebesgue integration is desirable.

Syllabus

No syllabus information is available yet.

Lecturer

  • AV

    Professor Alexander Veretennikov

    University
    University of Leeds

Bibliography

No bibliography has been specified for this course.

Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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