- Unit Coordinator: François Delarue
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of Côte d'Azur
- Language: English
- Aims:
The course has two purposes. The first one is to provide the basic knowledge in stochastic control, control for discrete and continuous processes, dynamic programming principle, dynamic programming equation, Hamilton-Jacobi-Bellman equation.
The second part of the course will address interacting particle systems, as some of them are now currently used in the modelling of large neural networks. Applications to self-organisation and phase transition in neuroscience will be considered and, in connection with the first part of course, some learning methods will be discussed as well.
- Content:
- Stochastic control
- Dynamic programming principle
- HJB equation, interacting particle system
- Mean field models
- Learning methods
- Pre-requisites:
Probability with measure theory, optimization, stochastic calculus
- 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
