Department of Information & Communication Systems Engineering
University of the Aegean

Department of Information
& Communication Systems Engineering

Information & Communication Systems Security
Information Systems
Artificial Intelligence
Computer & Communication Systems
Geometry, Dynamical Systems & Cosmology
Stochastic Calculus

Title: Stochastic Calculus
Lesson Code: 321-3751
Semester: 3
Theory Hours: 3
Lab Hours: 2
Faculty: Leros Asimakis
Content outline

Review of basic random variables.Definition of stochastic processes. The Bernoulli, Poisson and birth-and-death processes. Simulation of discrete and continuous random variables. Markov chains, Chapman-Kolmogorov equations, classification of states, limiting probabilities. Mean time spent in transient states.

Learning outcomes

Upon completion of the course, the student will be able to:

  • understand random arrivals
  • perform probability calcucations in Bernoulli and Poisson processes
  • understand modelling of discrete-event systems by Markov chains
  • perform calculation and interpretation of limiting probabilities
  • generate random variates
  • perform basic calculations of reliability and availability


Basic Textbooks

1. T. Daras, P. Sypsas, “Stochastic Processes’’ (in Greek).
2. O. Chrysafinou, “Introduction to Stochastic Processes’’ (in Greek).

Additional References

1. S. Ross, Introduction to probability models, Academic Press, 2002.
2. S. Karlin and H.M. Taylor, A first course in stochastic processes, Academic Press, 1975.

Learning Activities and Teaching Methods

5 in-class quizzes

Final written exam

Lectures: 36 hrs

Recitation: 26 hrs
Personal study: 60 hrs
Quizzes: 3 hrs
Final exam: 3 hrs
Total: 128 hrs (5 ECTS)

Assessment/Grading Methods


Activity Semester workload

39 hours

Review-Problem Session ασκήσεις  26 hours
Personal study 57 hours
Final exams 3 hours
Σύνολο μαθήματος   125 hours (5 ECTS)


Language of Instruction
Greek, English (for Erasmus students)
Μode of delivery

Weekly class meetings
Weekly recitations (devoted mostly to problem solving)

  • Σημειώσεις μαθήματος
  • 1ο Σύνολο Ασκήσεων
  • 2ο Σύνολο Ασκήσεων
  • 3ο Σύνολο Ασκήσεων
  • 4ο Σύνολο Ασκήσεων
  • Βαθμολογία 1ης-2ης άσκησης
  • Βαθμολογία 3ης-4ης άσκησης

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