Overall Objectives
Research Program
Application Domains
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
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Section: Research Program

Stochastic models

The link between stochastic processes and kinetic equations is a domain already present in our research (H. Byrne and D. Drasdo, Individual-based and continuum models of growing cell populations: a comparison, J. Math. Biol, 2009) [53] and that we aim at developing further. They can be viewed either as complementary approaches, useful to take into account different scales (smaller scales for stochastic models, larger scales for mean-field limits), or even as two different viewpoints on the same problem [52] , enriching each other. Neuroscience is a domain where this is particularly true because noise contributes significantly to the activity of neurons; this is particularly true for networks where mean field limits are derived from stochastic individual-based models and lead to fundamental questions on well-posedness and behaviours of the system (Cáceres, Carrillo, Perthame J. Math. Neurosci. 2011; Pakdaman, Perthame, Salort Nonlinearity 2010). One strength and originality of our project is our close connections and collaborations not only with probability theorists but also with statisticians.