Stochastic Methods

This course offers an in-depth exploration of stochastic methods, focusing on both theoretical foundations and practical applications. Topics covered include random variables and vectors, expectation, variance, conditional probability, Monte-Carlo methods, Markov chains, random networks, counting processes, simulation methods, and continuous-time Markov Chains. Through lectures, exercises, and practical problems, students will gain the skills necessary to tackle complex problems involving stochastic processes.

The primary objective of this course is to provide a comprehensive understanding of stochastic methods and their applications. Students will learn to model, analyze, and solve problems involving randomness and uncertainty in various domains such as finance, biology, and engineering. By the end of the course, students will be able to:

• Understand and apply the principles and tools of probability theory.
• Develop and analyze stochastic processes, including Markov chains and Poisson processes.
• Utilize simulation techniques, such as Monte Carlo methods, for practical problem-solving.
• Implement stochastic modeling in real-world scenarios such as queuing systems

In presenza

The course employs a variety of learning methods to ensure a thorough understanding of stochastic methods:

• Lectures: Detailed theoretical presentations of key concepts.
• Lecture Notes: Comprehensive notes provided for each lecture to aid in studying and reference.
• Tutorials: Hands-on exercises and problems with implementation in Python.
• Discussions: Sessions for clarifying doubts and discussing learning progress.

Assessment in this course will be based on:

• In-class quizzes (20%)
• Written exams: midterm (40%) and final (40%)