Introduction course to Piecewise Deterministic Markov Processes and Applications to Neuroscience

19 Feb Introduction course to Piecewise Deterministic Markov Processes and Applications to Neuroscience

This mini-course aims to provide an introduction to piecewise deterministic Markov processes (PDMP) applied to neuroscience. The PDMP formalism was introduced in the 1980s [2, 3], it is both simpler than the formalism of diffusion processes and, unlike the latter, PDMPs can directly be understood from ordinary differential equations. PDMPs have recently been applied in modeling for neuroscience especially in neuronal models [1, 4, 5]. The purpose of this course is to introduce PDMPs, to explain how to simulate and analyze them. We will apply these processes to spiking models for a single or for a network of neurons.

PROGRAMME:

1.Basic definitions: Exponential distribution, Poisson process, PDMP, Markov processes.
2.Simulation: Two properties of the Exponential distribution, exact simulation, Gillespie algorithm.
3. Analysis: recsaling, law of large number, central limit theorem.

Info: https://www.bcamath.org/en/courses/2019-06-10-bcam-course