Stochastic Processes

Course Description

Conditional and marginal distributions of random variables. Functions of random variables and vectors. Modeling of binomial, Poisson, exponential and normal random variables. Markov chains. Stochastic processes. Markov processes. Poisson and similar processes. Gaussian processes. Kolmogoros?s equations. Spectral analysis of random processes. Processes in linear systems, filtration, estimation and prediction.

General Competencies

Learning advanced calculus of stochastic variables and vectors. Acceptance of concepts of stochastic processes

Learning Outcomes

  1. recognize the type and basic characteristic of the processes in the real environment
  2. use the technique of Markov chains in simple modeling
  3. recognize stochastic independence and learn to measure dependence of various processes
  4. calculate the main parameters of the processes with known distribution type
  5. analyze advanced models of stochastic experiments
  6. apply stochastic technique in modeling of real linear systems

Forms of Teaching

Lectures

Lectures are organized through two cycles. The first cycle consists of 7 weeks of classes and mid-term exam, a second cycle of 6 weeks of classes and final exam. Classes are conducted through a total of 15 weeks with a weekly load of 3 hours.

Exams

Mid-term exam in the 8th week of classes and final exam in the 15th week of classes.

Consultations

Consultations are held one hour weekly according to arrangement with students.

Seminars

Student can choose the topic of an essay and write it during the term.

Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Comment: Percent of Grade
Quizzes 0 % 20 % 0 % 20 %
Mid Term Exam: Written 0 % 40 % 0 %
Final Exam: Written 0 % 40 %
Exam: Written 0 % 80 %

Week by Week Schedule

  1. Random variables and vectors. Conditional and marginal distributions. Independence. Conditional expectation. Charecteristic function.
  2. Basic distributions. Binomial, Poisson, exponential and normal distribution.
  3. Generating function. Properties and applications. Polinomial schema.
  4. Random walk. Recursive equations. Two player game. Generalized random walk.
  5. Recurrent events. Markov chains. Matrices of transition probabilities.
  6. Stationary probabilities. Classification of states of Markov chains.
  7. Stochastic processes. Finite-dimensional distributions. Classification of processes. Independence. Correlation functions.
  8. Exam.
  9. Poisson process. Construction of Poisson process. Sum and decomposition of Poissonovih processes.
  10. Homogenous Markov processes. Kolmogorov’s equations. Birth and death process.
  11. Brownian motion. Kolmogorov’s equations for diffusion processes.
  12. Spectral density and correlation function. White noise. Ergodicity.
  13. Linear systems. Transformation of processes. Connection to autocorrelation and cross-correlation functions.
  14. Best estimation criteria. Wiener filter. Prediction of processes.
  15. Exam.

Study Programmes

Control Engineering and Automation -> Electrical Engineering and Information Technology (Profile)

Electrical Engineering Systems and Technologies -> Electrical Engineering and Information Technology (Profile)

Electrical Power Engineering -> Electrical Engineering and Information Technology (Profile)

Electronic and Computer Engineering -> Electrical Engineering and Information Technology (Profile)

Electronics -> Electrical Engineering and Information Technology (Profile)

Information Processing -> Information and Communication Technology (Profile)

Telecommunication and Informatics -> Information and Communication Technology (Profile)

Wireless Technologies -> Information and Communication Technology (Profile)

Software Engineering and Information Systems -> Computing (Profile)

Computer Engineering -> Computing (Profile)

Computer Science -> Computing (Profile)

Literature

N. Elezović (2010.), Stohastički procesi, FER, interna skripta
J. Medhi (1982.), Stochastic Processes, WEL
P. Z. Peebles (1987.), Probability, random variables and random signal principles, McGraw-Hill
E. P. C. Kao (1997.), An Introduction to Stochastic Processes, Wadsworth Publishing Company

Grading System

4 ECTS
L0 English Level
L1 e-Learning
45 Lecturers
0 Exercises
0 Laboratory exercises

Grading

85 Excellent
70 Very Good
55 Good
45 Acceptable