Modules

Prerequisites

Contents

• Markov processes, discrete and continuous in time, • communication classes and asymptotic behaviour of Markov chains • processes with independent and stationary increments, martingales • stopping times and stopping theorems, optimal stopping • applications from finance, science and engineering

Learning outcomes

After successfully completing the module, students • are familiar with the basic concepts and ideas behind random processes, • know models and methods for time-dependent random phenomena, • are prepared for studying advanced topics in stochastics • have experience in autonomously doing research based on specific applications.

Assessment

• Written examination, 90 min. OR • Oral examination, 30 min. In the first lecture it will be anounced, if the examination will be offered in written or oral form.

Remarks

• Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in the complex „Stochastik“ • Study programme Mathematik B.Sc.: Compulsory elective module in complex „Specialisation“, in limited extend • Study programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in complex „Specialisation“, in limited extend • Study programme Artificial Intelligence M.Sc.: Compulsory elective module in complex „Knowledge Acquisition, Representation, and Processing“ • Study programme Informatik B.Sc.: Compulsory elective module in field of application „Mathematik“ • Study programme Informatik M.Sc.: Compulsory elective module in field of application „Mathematik“ • Study programme Mathematics M.Sc.: Compulsory elective module in complex „Stochastics“ • Study programme Mathematical Data Science M.Sc.: Compulsory elective module in complex „Advanced Mathematical Methods in Data Science“