Stochastic Modelling

Course Description

In the introductory chapter, the generation of pseudorandom numbers will be studied. The properties of the most important types of distributions occurring in engineering are studied and the models in which they occur are examined. These models are simulated using a computer. Similar techniques is used in modelling finite Markov chains and the Poisson process. The Monte Carlo method is studied. Finally, the problem of variance reduction in sampling is addressed.

Learning Outcomes

  1. Improve knowledge about the basic laws of random events
  2. Learn to distinguish the most important random variables according to their properties
  3. Model important distributions
  4. Model complex situations in which randomness occurs
  5. Model stochastic processes and Markov chains
  6. Apply the basic techniques of the Monte Carlo method

Forms of Teaching

Lectures

Seminars and workshops

Independent assignments

Week by Week Schedule

  1. Pseudorandom number generators, Statistical analysis of simulated data
  2. The sample mean and sample variance, Interval estimates of a population mean, Goodnes of fit test
  3. The inverse transform method, Poisson distribution
  4. Bbinomial distribution, Geometric distribution, Negative binomial distribution, Hypergeometric distribution
  5. The inverse transform algorithm, The polar method for genetrating normal random variables
  6. Generatring random vectors, Multinormal distribution
  7. Exponential distribution, Cauchy distribution, Gama and beta distributions, Weibul distribution
  8. Midterm exam
  9. Normal distribution, Lognormal distribution, Chi-square distribution, Student t-distribution, F distribution
  10. Finite Markov chain, First exit time
  11. Generating a Poisson process, Generating a nonhomogeneous Poisson process
  12. Using random nubers to evaluate integrals, The sample mean Monte Carlo methods, Monte Carlo methods for linear systems
  13. Importance sampling, Correlated sampling, Stratisfied sampling, Biased estimators
  14. Seminar
  15. Final exam

Study Programmes

University graduate
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Literature

(.), Neven Elezović, Stohastičko modeliranje - skripta,
(.), Nedžad Limić, Monte Carlo simulacije slučajnih veličina, nizova i procesa, Zagreb, Element 2002,,
(.), M. A. Pinsky, S. Karlin, An Introduction to Stochastic Modeling, Elsevier 2011,
(.), S. M. Ross, Introduction to Probability Models, 10th ed., Elsevier 2010,

For students

General

ID 222785
  Winter semester
5 ECTS
L3 English Level
L1 e-Learning
45 Lectures