Dr Umut Cetin COL 6.08

This course is available on the MSc in Financial Mathematics, MSc in Risk and Stochastics, MSc in Statistics (Financial Statistics) and MSc in Statistics (Financial Statistics) (Research). This course is available with permission as an outside option to students on other programmes where regulations permit.

Students must have completed Stochastic Processes (ST409).

Markov property and transition functions. Feller processes. Strong Markov property. Martingale problem and stochastic differential equations, relation with partial differential equations. Diffusion processes. Affine processes. Piecewise deterministic Markov processes. Selection of topics from filtering and statistics of diffusion processes. Applications.

20 hours of lectures and 10 hours of seminars in the LT.

A weekly set of homework will be set. Students are not expected to submit this homework but will go over the exercises in the following seminar with the lecturer. Students will also complete one or two sets of formative coursework during the year which will be marked. Feedback will be provided.

An Introduction to Markov Processes and Their Applications. Lecture Notes by Umut Cetin
I. Karatzas and S. Shreve: Brownian Motion and Stochastic Calculus. Springer
D. Revuz and M. Yor: Continuous Martingales and Brownian Motion. Springer
K.L. Chung and. J. Walsh: Markov Processes, Brownian Motion and Time Symmetry. Springer

Exam (80%, duration: 2 hours) in the main exam period.
Project (20%) in the ST.