Learning advanced calculus of stochastic variables and vectors. Acceptance of concepts of stochastic processes
- recognize the type and basic characteristic of the processes in the real environment
- use the technique of Markov chains in simple modeling
- recognize stochastic independence and learn to measure dependence of various processes
- calculate the main parameters of the processes with known distribution type
- analyze advanced models of stochastic experiments
- apply stochastic technique in modeling of real linear systems
Forms of Teaching
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.
|Type||Threshold||Percent of Grade||Threshold||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
- Random variables and vectors. Conditional and marginal distributions. Independence. Conditional expectation. Charecteristic function.
- Basic distributions. Binomial, Poisson, exponential and normal distribution.
- Generating function. Properties and applications. Polinomial schema.
- Random walk. Recursive equations. Two player game. Generalized random walk.
- Recurrent events. Markov chains. Matrices of transition probabilities.
- Stationary probabilities. Classification of states of Markov chains.
- Stochastic processes. Finite-dimensional distributions. Classification of processes. Independence. Correlation functions.
- Poisson process. Construction of Poisson process. Sum and decomposition of Poissonovih processes.
- Homogenous Markov processes. Kolmogorov’s equations. Birth and death process.
- Brownian motion. Kolmogorov’s equations for diffusion processes.
- Spectral density and correlation function. White noise. Ergodicity.
- Linear systems. Transformation of processes. Connection to autocorrelation and cross-correlation functions.
- Best estimation criteria. Wiener filter. Prediction of processes.