Stochastic Processes (MAGIC065) |
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 GeneralThis course is part of the MAGIC core. SemesterAutumn 2011 (Monday, October 10 to Friday, December 16) Timetable
PrerequisitesIt 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.
Lecturers
Students
Bibliography
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.) Assessment1. 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
Exam questions 2011 for two parts of the course
FilesFiles marked L are intended to be displayed on the main screen during lectures.
Recorded LecturesPlease log in to view lecture recordings. |