Courses

Stochastic Processes

General

Course Contents

A brief review of key elements of probability theory and distributions. Basic concepts of Random Processes. Discrete- /continuous-time and discrete/continuous state space models of processes. Arrivals in discrete time: Bernoulli process. Arrivals in continuous time: Poisson process. Markov chains: Definition of Markov models. Transition probability tables. Chapman-Kolmogorov equations. Markov Chains: Periodicity. Balance equations.
Stochastic signals: definition, classification. Expected values: Mean, autocorrelation. Stationarity. Ergodicity. Autocorrelation and crosscorrelation properties. Spectral power density. Linear system response to stochastic input. Gaussian process. White noise. Applications and examples.

Educational Goals

The course is designed as an introduction to the mathematical modeling of the uncertainty in production systems problems. Students are invited to study the basic principles of stochastic process analysis by applying mathematical modeling, analysis and problem solving that take into account randomness in systems variables. After a brief review of probability theory, it focuses on processes of an “arrival” or “completion” nature as well as processes that evolve over time with possible dependencies on the past. Stochastic signals are defined and classified, the basic concepts of stationarity and ergodicity are introduced, while systems with stochastic inputs in various domain representations (t, ω, s) are examined and analyzed. On completion of the course, students should be able to recognize and analyze sequences of events that occur over time and, understand and apply basic methodologies of stochastic process analysis by modeling the relative problems. The course also provides the basic background for understanding and implementing a number of applications related to communication and control signals and systems with stochastic inputs. Moreover, is a basic prerequisite for advanced courses in organization of production and in operations research as well as in automation engineering.

General Skills

Research, analysis and synthesis of data and information, using corresponding technologies, Adaptation to new situations, Decision making, Working in an international environment, Independent work, Teamwork – distribution of responsibilities, Working in an interdisciplinary environment, Practicing criticism and self-criticism, Promoting free, creative and inductive thinking.

Teaching Methods

Lectures, Exercises, Online guidance, Projected Presentations, E-mail communication, Online Synchronous and Asynchronous Teaching Platform (moodle).

Students Evaluation

Assessment Language: English / Greek
The grade of the course is formed 100% by a written final examination including problem solving, graphs, diagrams and calculations based on data.

Recommended Bibliography

1. Introduction to Probability Models, 11th E, Sheldon Ross, Academic Press, ISBN-13: 9780124079489.
2. PROBABILITY, RANDOM VARIABLES, AND STOCHASTIC PROCESSES, 4th E, Athanasios Papoulis, S. Unnikrishna Pillai, ISBN-13: 978-0071226615.
3. Introduction to Stochastic Processes with R, Robert Dobrow, Wiley, ISBN-13: 9781118740651.