Announcements


The two parts of the course - see the syllabus - will be presented in parallel: part 1 on Friday and part 2 on Monday. (In particular, we start on Monday 10.10.2011 with the first lecture from part 2.) There is no stone wall between the two parts. Some mild cross-references will remain, however, the idea is that each part may be attended (and assessed) independently, although, naturally, we encourage the audience to attend both parts.
The team
PS. Please, do not forget to register on each lecture you attend.

Forum

General


This course is part of the MAGIC core.

Semester

Autumn 2011 (Monday, October 10 to Friday, December 16)

Timetable
  • Mon 11:05 - 11:55
  • Fri 10:05 - 10:55

Lecturers


Alexander Veretennikov (main contact)
Email veretenn@maths.leeds.ac.uk
Phone (0113) 3435183
vcard
Photo of Alexander Veretennikov
Grant Lythe
Email grant@maths.leeds.ac.uk
Phone (0113) 3435132
vcard
Photo of Grant Lythe
Carmen Molina-Paris
Email C.Molina-Paris@maths.leeds.ac.uk
Phone (0113) 3435151
vcard
Photo of Carmen Molina-Paris
Jochen Voss
Email voss@seehuhn.de
Phone (0113) 3435125
vcard
Photo of Jochen Voss


Students


Photo of Hassan AlJohani
Hassan AlJohani
(Leeds)
Photo of Badr Almohaimeed
Badr Almohaimeed
(Manchester)
Photo of Jenna Birch
Jenna Birch
(Liverpool)
Photo of Shanyun Chu
Shanyun Chu
(Liverpool)
Photo of Zhen Cui
Zhen Cui
(Exeter)
Photo of Fan Fei
Fan Fei
(Liverpool)
Photo of Kavita Gangal
Kavita Gangal
(Newcastle)
Photo of Jhonny Gonzalez
Jhonny Gonzalez
(Manchester)
Photo of Christian Groh
Christian Groh
(Leeds)
Photo of Haochen Hua
Haochen Hua
(Liverpool)
Photo of Javed Hussain
Javed Hussain
(York)
Photo of Julian Mak
Julian Mak
(Leeds)
Photo of David Maycock
David Maycock
(East Anglia)
Photo of Sophie Reed
Sophie Reed
(Southampton)
Photo of Joseph Reynolds
Joseph Reynolds
(Leeds)
Photo of Xavier Riedinger
Xavier Riedinger
(Exeter)
Photo of Yuan Si Cong
Yuan Si Cong
(Manchester)
Photo of Falconer Steven
Falconer Steven
(Manchester)
Photo of Kuanhou Tian
Kuanhou Tian
(Loughborough)
Photo of Elliott Tjia
Elliott Tjia
(Liverpool)
Photo of Thomas Ward
Thomas Ward
(Nottingham)
Photo of Derek Watson
Derek Watson
(Southampton)
Photo of Thomas Wicks
Thomas Wicks
(Nottingham)
Photo of Robert Wilkinson
Robert Wilkinson
(Liverpool)
Photo of Yue  Wu
Yue Wu
(Loughborough)
Photo of Magdalena Zajaczkowska
Magdalena Zajaczkowska
(Loughborough)


Prerequisites


It is desirable to know something about Markov chains.

Syllabus


=======================
Fridays Lythe (weeks 1-4) Voss (weeks 5-8) Molina-Paris (weeks 9-10)
=======================
1-1 Gambler's ruin. Discrete random variables. Continuous random variables.
1-2 Random walk, discrete-time Markov chains.
1-3 Branching processes. Continuous-time Markov Chains. Birth and death processes. Gillespie algorithm.
1-4 Stationary distributions, quasi-limiting distributions.
1-5 Stochastic processes. Wiener process. Diffusion equation.
1-6 The reflection principle and passage times. Conditional hitting probability.
1-9 Applications to immunology.
======================
Mondays (Veretennikov)
======================
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.

Bibliography


An Introduction to Stochastic ModellingTaylor and Karlin
Introduction to the Theory of Random ProcessesKrylov
Stochastic Calculus and Financial ApplicationsJ Michael Steele
Diffusions, markov processes, and martingalesRogers and Williams
Brownian motion and stochastic calculusKaratzas and Shreve
Brownian motionMörters, Peres, Schramm and Werner
Handbook of Brownian motion: facts and formulaeBorodin and Salminen


Note:

Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will 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.)

Assessment


1. There will be one assignment consisting of two parts - for two parts of the module - and each of which will include five of six questions.
2. It is allowed to take an exam for one part of the course, Friday or Monday, or both. (For each part you would get a half of the total amount of credits.) To sit either part, you have to choose four questions from this part. I.e., to sit the first part, you choose four questions from the first part and to sit both parts you choose four questions FROM EACH PART, altogether EIGHT.
3. The assignment will be available from Friday 16.12.2011. Your reports are due by 16.01.2012. We then intend to return your marks (at pass/fail scale as suggested by Magic) by 01.02.2012.
4. To pass this exam successfully, you have to satisfy the requirement in item 2 above and solve reasonably well a bit more than half of all chosen questions, that is, more than 2/4 for one part and 4/8 for both parts; it roughly corresponds to 60

Assignments


Exam questions 2011 for two parts of the course

Files:Exam paper
Deadline: Monday 16 January 2012 (1012.1 days ago)
Instructions:See "Assessment". Max 20 is available for the whole course (Part I + Part II). Each part admits max 10 credits.