- Understand the basic principles of stochastic processes
- Learn to distinguish between stochastic processes according to their properties.
- Understand the characteristic lack of memory in different cases
- To interpret the behavior of the process in accordance with the theoretical laws.
- Determine the probability of prominent events related to stochastic processes.
- Learn to model simple problems using stochastic techniques.
- Apply stochastic techniques in the analysis of various systems.
Forms of Teaching
Week by Week Schedule
- Conditioning on a random variable; Conditioning on a sigma-field; Conditional expectation and distributions.
- Sums of independent random variables; Stoping times Wald identities; Generating functions.
- Random walks; Probability of ruin; Recurrent events.
- Foundations and examples; construction of Markov chains; Transition probabilities and the Chapman-Kolmogorov equation; Stopping times and strong Markov property; Absorbing states; transient and recurrent states; Branching processes.
- Limit theorems and stationary distributions; State classifications; Ergodic theorems; Finite-dimensional distributions of processes; Moments; correlation and covariation functions; Classes of processes: Markov, homogenous Markov, weak/strong stationary, independent increment processes; Transition and density matrix and Chapman-Kolmogorov equation for Markov processes.
- Homogeneous Poisson processes; Memoryless property.
- Poisson processes and uniform, exponential and binomial distributions; Nonhomogeneous Poisson processes; Mixed and Compound Poisson Processes; Poisson arrivals.
- Midterm exam.
- Basic concepts and examples; Transition probabilities and rates; Birth and death processes; Kolmogorov differential equations; Stationary state probabilities; Ergodic theorems.
- Renewal Functions; Excess life, current life and total life; Strong laws of large numbers; Recurrence times; Terminating renewal processes; Stationary renewal processes; Alternating Renewal Processes.
- Basic concepts; The Erlang model, M/M/1 and M/M/c queue.
- Loss systems: M/M systems; Waiting systems: M/G and G/M models; Network of queueing systems.
- Introduction; Properties of Brownian motion; Multidimensional and conditional distributions; First passage times.
- Transfornmations of the Brownian motion; Brownian motion with drift; White noise; Diffusion processes.
- Final exam.
Computing (study)Elective Courses (6. semester)
Electrical Engineering and Information Technology (study)Elective Courses (6. semester)
(.), Neven Elezović, Stohastički procesi,
L3 English Level
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