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, expectation, variance, conditional probability, Markov chains, random networks, Poisson processes, simulation methods, continuous-time stochastic processes, stochastic modeling, and optimization. Through lectures, practical examples, and projects, 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 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 and optimization techniques in real-world scenarios.

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.
• Practical Sessions: Hands-on exercises and examples to apply theoretical knowledge.
• Projects: Real-world case studies and projects to develop and implement stochastic models.
• Discussions: Interactive sessions to clarify doubts and discuss applications of stochastic methods.

Assessment in this course will be based on:

• Assignments and Projects: Regular homework assignments and group or individual projects that involve real-world applications of stochastic methods.
• Exams: Midterm and final exams to test understanding of key concepts and problem-solving abilities.