CV Information - دانشگاه صنعتی امیرکبیر

Stochastic Processes

Session 1 Introduction to the course, structure, expectations and assessment methods Review of basic concepts of probability (quick review)Session 2 Formal definition of a stochastic process Time index, state space, joint distributions Classic and applied examples
Session 3 Classification of stochastic processes Discrete/continuous, discrete/continuous timeSession 4 Introduction to discrete-time Markov chains Markov properties and model assumptions
Session 5 Transition matrix and path analysis Applied examples (system, user behavior, inventory)Session 6 Transient and long-term distributions Stable distribution and conditions of existence
Session 7 Case study/numerical analysis of Markov chains Managerial and analytical interpretation of resultsSession 8 First quiz
Session 9 Introduction to the Poisson process Definition, assumptions and applications Session 10 Inter-event time distribution Poisson process HomogeneousSixth deadline for determining and approving selected papers for implementation
Session 11 Exponential distribution Applications of the Poisson processSession 12 Simulation of the Poisson process Case study/event-driven applications
Session 13 Quiz 2Session 14 Introduction to continuous-time Markov chains
Session 15 Rate matrix Examples and exercises in continuous-time MarkovSession 16 Analysis in continuous-time Markov Kolmogorov equations
Session 17 Examples and classroom exercises in continuous-time MarkovSession 18 Case study in continuous-time Markov Interpretation of results for decision-making in continuous-time Markov
Session 19 General Markov processesSession 20 Examples and exercises in general Markov
Session 21 Case study in general Markov processesSession 22 Quiz 3
Session 23 Introduction to the Wiener process (Brownian motion) Properties and interpretationSession 24 Exercises and examples of Brownian motion Simulation of Brownian motion
ession 25 Case study of Brownian motion Session 26 Analysis and interpretation of results
Conclusion
Presentation of projects