Introduction to Piecewise Deterministic Markov Processes and Applications to Neuroscience

Date: Mon, Jun 10 - Fri, Jun 14 2019

Hour: 10:00

Location: BCAM Seminar room

Speakers: Fabien Campillo (Inria Montpellier)

DATES: 10-14 June 2019 (5 sessions)
TIME: 10:00 - 12:00 (a total of 10 hours)
LOCATION: BCAM Seminar room

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.


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

This course will be illustrated by Python, or possibly Julia, notebooks. Those who master R (or Matlab) can use these languages.

[1] P. C. Bressloff. Waves in Neural Media: From Single Neurons to Neural Fields. Springer New York, 2013.
[2] M. H. A. Davis. Piecewise-deterministic Markov processes: A general class of non-diffusion stochastic models. Journal of the Royal Statistical Society. Series B (Methodological), 46(3):353-388, 1984.
[3] M. H. A. Davis. Markov Models and Optimization. Springer, 1993.
[4] W. Gerstner, W. Kistler, R. Naud, and L. Paninski. Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition. Cambridge University Press, 2014.
[5] R. Rudnicki and M. Tyran-Kamińska. Piecewise Deterministic Processes in Biological Models. Springer- Briefs in Applied Sciences and Technology. Springer International Publishing, 2017.

*Registration is free, but mandatory before June 7th: So as to inscribe go to and fill the registration form. Student grants are available. Please, let us know if you need support for travel and accommodation expenses when you fill the form.




Confirmed speakers:

Fabien Campillo (Inria Montpellier)