t.BA.WI.STOP.19HS (Stochastic Processes)
Module: Stochastic Processes
This information was generated on: 26 September 2021
No.
t.BA.WI.STOP.19HS
Title
Stochastic Processes
Organised by
T IDP
Credits
4

### Description

Version: 2.0 start 01 February 2020

#### Short description

The module introduces students to the basic principles of stochastic processes. Discrete-time and continuous-time Markov processes with finite state space and point processes are introduced.

#### Module coordinator

Mildenberger Thoralf (mild)

#### Learning objectives (competencies)

 Objectives Competences Taxonomy levels You have understood the basic concept of stochastic processes (modelling of dynamic processes using dependent random variables). F, M K1, K2 You know time- and state-discrete Markov chains and their most important properties. You can recognize for which problems they are suitable for modeling. You know the most important methods for analyzing both the behavior for a small number of steps and the long-term behavior, and you can use these methods to solve new problems. F, M K1, K2, K3 You know different simple types of point processes and their most important properties. You know the most important methods for analyzing behavior and can use them to solve new problems. F, M K1, K2, K3 You know time-continuous, state discrete Markov processes and their most important properties. You know the most important methods for analyzing behavior and can apply them to solve new problems. F, M K1, K2, K3 You can implement calculations and simulations for concrete problems in a programming language (e.g. R). F, M K5

#### Module contents

Markov chains with finite state space

• Basic concepts: transition probabilities, state distributions, properties of states

• Analysis of transitions and duration of stay

• Costs with finitely many time steps and costs in the long run (asymptotics)

• Markov Chain Monte Carlo as a simulation method based on Markov chains

Point processes

• Poisson processes

• Renewal processes

• Cumulative processes

Time-continuous Markov processes with finite state space

• Basic concepts: transition, rate and generator matrices, state distributions

• Analysis of transitions, duration of stay

• Costs with finitely many time steps and costs in the long run (asymptotics)

#### Teaching materials

Lecture notes, slides presented in class, exercises

#### Supplementary literature

• Kulkarni, V.G. (2011). Introduction to Modeling and Analysis of Stochastic Systems, Second Edition, Springer.

• Waldmann, K.H., Stocker, U.M. (2004). Stochastische Modelle. Eine anwendungsorientierte Einführung, Springer.

WaSt 2

#### Teaching language

(X) German ( ) English

( ) Yes (X) No

#### Module structure

(Is filled in by the administration)
For more details please click on this link: T_CL_Modulauspraegungen_SM2025

#### Exams

 Description Type Form Scope Grade Weighting Graded assignments during teaching semester (solution of several practical execises) 40% End-of-semester exam 60%

#### Legal basis

The module description is part of the legal basis in addition to the general academic regulations. It is binding. During the first week of the semester a written and communicated supplement can specify the module description in more detail.
Course: Stochastische Prozesse - Vorlesung
No.
t.BA.WI.STOP.19HS.V
Title
Stochastische Prozesse - Vorlesung

### Note

• No module description is available in the system for the cut-off date of 01 August 2099.