- Programme: RealMaths
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: Claude Bernard University Lyon 1
- Language: English
- Unit Coordinator: dr hab. inż. Wojciech Kempa, prof. PŚ
- ECTS Credits: 5
- Year: 2
- Campus: Silesian University of Technology
- Language: English
- Aims:
The aim of the course is to familiarize students with basic stochastic models used in technical, economic, and natural sciences, as well as with the basics of stochastic simulation.
- Content:
1. Fundamentals of the theory of stochastic processes.
2. Poisson processes (simple, compound and non-stationary)
3. Elements of renewal theory. The renewal process and the renewal equation.
4. Markov chains with discrete and continuous time parameters.
5. Basics of queueing theory.
6. The Galton-Watson branching process.
7. Basics of stochastic simulation.
- Unit Coordinator: Patricia Reynaud and Etienne Tanré
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of Côte d'Azur
- Language: English
- Delivery: In-class
- Aims:
This course aims at providing a deep understanding of the main stochastic models used in neurocognition (Markov Chains, Integrate and Fire, point processes) and addressed (at least for some of them) in the Stochastic Calculus course and to study their mathematical properties.
The pros and cons of each of them is discussed, especially in terms of the modeling and the statistical inference of real data.
This course is taught by a teaching staff member of the Master Programme Mod4NeuCog at UCA
- Content:
• Stochastic models in neurocognition, statistical inference
• Statistical inference - Pre-requisites:
Statistics
- 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.
