Probability Methods in Engineering II

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Technical Mathematics

Synopsis:

Identification course with stochastic models, most frequently used in engineering applications. The course is pay to application of markovian processes in reliability and safety stochastic models, modelling of queueing systems, time series analysis.

Requirements:

The basic knowledge of probability theory and mathematical statistics is supposed.

Syllabus of lectures:

1

Random process, characterisation

2

Stationarity, examples of random processes

3

Poisson process

4

Renewal processes, ergodicity

5

Markov process with discrete time

6

Classification of states, stationary distribution

7

Markov process with continuous time

8

Kolmogorov differential equations

9

Queueing models and theirs classification

10

Application to reliability modelling

11

Time series, Box-Jenkins methodology

12

AR. MA , ARMA models

13Decomposition of time series

14

Stochastic simulation

Syllabus of tutorials:

1

Random process, characterisation

2

Stationarity, examples of random processes

3

Poisson process

4

Renewal processes, ergodicity

5

Markov process with discrete time

6

Classification of states, stationary distribution

7

Markov process with continuous time

8

Kolmogorov differential equations

9

Queueing models and theirs classification

10

Application to reliability modelling

11

Time series, Box-Jenkins methodology

12

AR. MA , ARMA models

13Decomposition of time series

14

Stochastic simulation

Study Objective:

Study materials:

Mukhopadhyay N.: Probability and statistical inference. M. Dekker Inc., 2001.

Ulrich M.: Základy teorie náhodných procesů, ČVUT Praha 1968

Dohnal G.: Teorie hromadné obsluhy, učební texty na http://d.nipax.cz/tho

Basawa I.V., Prakasa Rao B.L.S.: Statistical inference for stochastic processes. Academic Press, 1980

Mukhopadhyay N.: Probability and statistical inference. M. Dekker Inc., 2001.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: