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This course is part of the MAGIC core.


Autumn 2012 (Monday, October 8 to Friday, December 14)


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


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


It is desirable to know something about Markov chains.


Mondays 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.
Fridays (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.


Alexander Veretennikov (main contact)
Phone (0113) 3435183
Photo of Alexander Veretennikov
Grant Lythe
Phone (0113) 3435132
Photo of Grant Lythe
Carmen Molina-Paris
Phone (0113) 3435151
Photo of Carmen Molina-Paris
Jochen Voss
Phone (0113) 3435125
Photo of Jochen Voss


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


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.)


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 07.01.2013. Your reports are due by 18.01.2012. We then intend to return your marks (at pass/fail scale as suggested by Magic) by 25.01.2013.
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

Magic 065 assignment 2012/2013

Files:Exam paper
Deadline: Friday 18 January 2013 (2586.7 days ago)

See Assessment rules. You have to open the Exam paper.

Recorded Lectures

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