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"Piecewise-deterministic Markov process" Benoite de Saporta (Video)

Mini-course

When a phenomenon is too complex to be modeled by a deterministic dynamic system of reasonable size, systems that include multiple regimes can be used. A well-defined theoretical framework is that of Piecewise-deterministic Markov Process (PDMP). In this mini-course, we will give an overview of the essential properties of PDMPs and advanced simulation techniques. This course will be accessible to the greatest number.

When a phenomenon is too complex to be modeled by a deterministic dynamic system of reasonable size, systems that include multiple regimes can be used. A well-defined theoretical framework is that of Piecewise-deterministic Markov Process (PDMP). They have many advantages, including the ability to use the powerful algorithms for solving ordinary differential equations that have been developed in recent decades between two regime changes.   However, they require new expertise to simulate the regime change times.
These systems (also known as hybrid stochastic systems) are frequently used in neuroscience models (see, for example, Bressloff's book, Stochastic Processes in Cell Biology, 2013). In particular, we find
  • ion channel models for which the closing or opening rate of each channel depends on the membrane potential. This is a typical example of a hybrid stochastic system.
  • synapse models.
Course content:
In this mini-course, we will give an overview of the essential properties of PDMPs and advanced simulation techniques. This course will be accessible to the greatest number.

Video 1   Video 2
Dates
Created on October 28, 2015