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Stochastic Processes
| Credits | 8 credit points |
| Instructors | Spieksma, F.M. (Universiteit Leiden) |
| Spieksma@math.leidenuniv.nl | |
| Aim | To provide a theoretical basis for the study of continuous-time stochastic processes. |
| Description | This course is an introduction to the theory of continuous-time stochastic processes. We plan to treat a number of classical results and to introduce two important classes of processes. These processes are so-called martingales and Markov processes. The main part of the course is devoted to developing fundamental results in martingale theory (first in discrete time and then in continuous time) as well as Markov process theory, with an emphasis on the interplay between the two. As a main illustration of the theory, we will study the fascinating properties of Brownian motion, an important process that is both a martingale and a Markov process. We also plan to discuss applications such as birth-death processes, which play an important role in queueing theory. If there is any time left, we can study other special cases of Markov processes. For instance, Brownian motion in higher dimensions, diffusions, Levy processes, continuous time Markov chains, counting processes. |
| Organization | Each class will be three 45 minute time slots. The last one will be devoted (in principle) to making exercises. |
| Examination | Homework exercises (compulsary!) and oral exam. The final grade is based on the results of both homework and oral exam. The deadline for each assignment is two weeks after the announcement, unless stated otherwise. |
| Literature | Lecture Notes. The lecture notes are an extended version of the Lecture Notes ``An Introduction to Stochastic Processes in Continuous Time'' by Harry van Zanten. |
| Prerequisites | We assume that students have a solid background in the measure theoretic foundations of probability theory, for instance by having attended the course on `Measure Theoretic Probability'. |
| Remarks | Homepage of the course: http://www.math.leidenuniv.nl/~spieksma/SPspring08.html |