Course content

Markov processes with discrete/continuous time-parameter and discrete/continuous state space,
including branching processes, Poisson processes, birth and death processes, and Brownian
motion. Queueing processes. Procedures for simulation of stochastic processes.

Learning outcome

1. Knowledge. The student has basic knowledge about stochastic processes in the time domain. The student has acquired more detailed knowledge about Markov processes with a
discrete state state space, including Markov chains, Poisson processes and birth and death
processes. The student also knows about queueing systems and Brownian motion, in addition to mastering the fundamental principles of simulation of stochastic processes and the
construction of Markov chain Monte Carlo (MCMC) algorithms.
2. Skills. The student is able to formulate simple stochastic process models in the time domain
and provide qualitative and quantitative analyses of such models.

Learning methods and activities

Lectures, exercises and semester project(s). Portfolio assessment is the basis for the grade awarded in the course. This portfolio comprises a written final examination (80%) and the semester project(s) (20%). The results for the constituent parts are to be given in %-points, while the grade for the whole portfolio (course grade) is given by the letter grading system. Retake of examination may be given as an oral examination. The lectures will be given in English if they are attended by students from the Master’s Programme in Mathematical
Sciences for International Students.

Compulsory assignments

• Exercise

Recommended previous knowledge

The course is based on TMA4240/TMA4245 Statistics or equivalent.

Course materials

Will be announced at the start of the semester.

Credit reductions