Stochastic calculus with applications to neuroscience

Unit Coordinator: Cédric Bernardin
Programme: Erasmus Mundus
ECTS Credits: 6
Semester: 1
Year: 2
Campus: University of Côte d'Azur
Language: English

The purpose of the course is to teach the basics of the theory of stochastic processes, which has become a standard tool in the modelling of biological neural networks.

The course will focus in particular on the Brownian motion, on stochastic calculus and on diffusion processes, with the integrate and fire model as a benchmark example.

Markov property and martingale theory will be also addressed in this framework, with possible extensions to some jump processes like those used in ion channel models.

  • Brownian motion
  • Stochastic Calculus
  • Diffusion Processes
  • Markov Property
  • Martingales
  • Integrate and fire model
  • Ion channel models

Probability with measure theory 


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