Entry requirements

Probability and Statistics

Learning outcomes

In order to pass the course the student should be able to

• use probabilistic arguments including conditional distributions and expectations;
• understand Poisson processes and models based on life-length distributions, and use them to assess risk and error;
• carry out basic modelling using Markov chains in discrete and continuous time;
• find probabilities and expected values for finite Markov chains using the principle of conditioning the first jump;
• review and apply Markov chains methods based on stationary and asymptotic distributions;
• use fundamental models of time series, in particular moving average and autoregressive models, and carry out covariance calculations in these cases;
• understand the basic principles of renewal theory and use them for performance calculations;
• present clear mathematical arguments.

Content

Stochastic processes, the Poisson process, life length models. Stochastic simulation. Markov chains in discrete and continuous time. Stationary and asymptotic distribution. Absorption probability, absorption time. Selected examples of applications of stochastic modelling, depending on study programme.

Instruction

Lectures, problem solving sessions and computer simulations.

Assessment

Written examination at the end of the course combined with assignments given during the course.