Stochastic processes

Course Unit Catalogue Last Updated: 05 November 2024

Code: DT0052
Unit Coordinator: Lucio Galeati
ECTS Credits: 6
Semester: 2
Year: 1
Campus: University of L'Aquila
Language: English
Aims:
Learning Outcomes

At the end of the course, the students should:

1. Developed the skills to model simple real problems and propose a solution;
2. Solve theoretical problems, using the appropriate mathematical tools;
3. Be able to read and understand other mathematical
texts on related topics;
4. Get a first flavour of the relevant research problems.
Content:
1. Discrete time processes: Markov chains in finite and countable space, limiting distribution;
2. Continuous time processes: density and distribution of into-event time for Poisson process, applications and extensions: e.g. birth-and-death processes, queues, epidemics;
3. Wiener processes and basic stochastic calculus: basic definitions and properties, Itô's formula, Stochastic Differential Equations.
Pre-requisites:
Probability Theory and Analysis
Reading list:

1. Markov Chains, J.R. Norris, Cambridge University Press;
2. Introduction to Stochastic Processes, G. Lawler, Chapman & Hall;
3. Basic Stochastic Processes, A Course Through Exercises, Z. Brzezniak and T. Zastawniak, Springer;
4. Probability and Random Processes, G. Grimmett and D. Stirzaker, 3rd Edition, Oxford University Press;
5. A Srst look at Rigorous Probability Theory, J. Rosenthal, World Scientific.

Course Unit