Master
2025/2026
Stochastic Models
Category 'Best Course for Career Development'
Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Category 'Best Course for New Knowledge and Skills'
Type:
Elective course (Data Analytics and Social Statistics)
When:
2 year, 3 module
Open to:
students of one campus
Instructors:
Ilya Petrov
Language:
English
ECTS credits:
3
Contact hours:
40
Course Syllabus
Abstract
This course guides students through practical stochastic methods to model, simulate, and analyze complex systems where uncertainty, interaction, and non-analytic behavior dominate. It connects probability paradigms with computational modeling to support understanding, research, and decision-making through simulation. The goal of the course is to enable students to design and implement Monte Carlo and agent-based models and to assess the usability and value of such models. Students will be able to identify when simulation is appropriate and to set up reproducible numerical experiments.
Learning Objectives
- To provide students with a solid theoretical foundation in stochastic paradigms, including key probabilistic models, Markov processes, and the mathematical principles underlying randomness and uncertainty.
- To develop students’ ability to critically evaluate a given problem and choose the most appropriate approach – analytical, statistical, or numerical – based on the system’s properties, available data, and desired outcomes.
- To equip students with hands‑on skills in implementing numerical methods (e.g., Monte Carlo simulations, iterative algorithms, and Bayesian updates) to simulate, analyse, and interpret the complex behaviour of stochastic systems in real‑world scenarios.
Expected Learning Outcomes
- Have the skill to meaningfully develop an appropriate model for the research question
- Have the skill to work with statistical software, required to analyze the data.
- Be able to develop and/or foster critical reviewing skills of published empirical research using applied statistical methods.
- Be able to criticize constructively and determine existing issues with applied linear models in published work .
- Be able to explore the advantages and disadvantages of stochasticity in the models and demonstrate how it contributes to the analysis.
- Be able to work with major linear modeling programs, especially R, so that they can use them and interpret their output.
- Have an understanding of the basic principles of stochastic models and lay the foundation for future learning in the area.
- Know modern extensions to stochastic modeling.
- Know the basic principles behind working with all types of data for using stochastic components in models.
- Know the theoretical foundation of stochastic processes.
Course Contents
- Understanding randomness
- Stein’s method and central limit theorems
- Conditional expectation and martingales
- Probability inequalities
- Discrete-time Markov chains
- Renewal theory
- Queueing theory (multiple class meetings)
Interim Assessment
- 2025/2026 3rd module0.2 * Homework Assignments + 0.5 * Final In-Class or Take-home exam + 0.2 * In-Class Labs + 0.1 * Quizzes
Bibliography
Recommended Core Bibliography
- Medhi, J. (2003). Stochastic Models in Queueing Theory (Vol. 2nd ed). Amsterdam: Academic Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=205403
- Meerschaert, M. M., & Sikorskii, A. (2011). Stochastic Models for Fractional Calculus. Berlin: De Gruyter. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=430094
Recommended Additional Bibliography
- Li, Q.-L. (2010). Constructive Computation in Stochastic Models with Applications : The RG-Factorizations. Beijing: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=374057