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General


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.

Semester

Autumn 2008 (Monday, October 6 to Friday, December 12)

Timetable

  • Tue 09:05 - 09:55
  • Thu 11:05 - 11:55

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


Alexander Veretennikov
Email A.Veretennikov@leeds.ac.uk
Phone (0113) 3435183
Photo of Alexander Veretennikov


Students


Photo of James Hook
James Hook
(Manchester)
Photo of Bjoern Huepping
Bjoern Huepping
(Birmingham)
Photo of Peng Lian
Peng Lian
(Loughborough)
Photo of Adam Skalski
Adam Skalski
(Lancaster)
Photo of James Springham
James Springham
(Leeds)
Photo of Qingfeng Wang
Qingfeng Wang
(Loughborough)
Photo of Jiayao Xie
Jiayao Xie
(Leicester)
Photo of Yi Zhang
Yi Zhang
(Liverpool)


Bibliography


No bibliography has been specified for this course.

Assessment



No assessment information is available yet.

No assignments have been set for this course.

Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
draft-beamer_i.pdf
1-10magic-v1-08a.pdfL
1-10magic-v1-08b-cor.pdfL
2-10draft-beamer_c1.pdfL
2-10draft-beamer_d.pdfL
3-10draft-beamer_e.pdfL
3-10lln.pdfL
5-10draft-beamer_e2a.pdfL
6-10draft-beamer_f.pdfL
7-10draft-beamer_g.pdfL
9-10draft-beamer_i2.pdfL
10draft-beamer_h.pdfL


Recorded Lectures


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