Stochastic Microscopic Models, the Wilson-Cowan Equation & the Neural Field Langevin Approximation
Sprache des Vortragstitels:
2nd International Conference on Neural Field Theory
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We consider a microscopic Markov chain model for large scale brain activity and show using general limit theorems for Hilbert space valued stochastic processes how the Wilson-Cowan equation arises as the limit of microscopic models for taking the number of neurons to infinity. We further present a central limit theorem that characterises the internal fluctuations of the model. The combination of these two results provides an ad-hoc argument to obtain a certain stochastic partial differential equation which is expected to be similar in dynamics than the microscopic jump models but far less complex. This equation, called the neural field Langevin approximation allows for a tractable analytical and numerical analysis. The neural field Langevin approximation, defines a stochastic process which is a second order approximation to the microscopic models and its moments are closely related to the second order approximations to the Wilson-Cowan equation in terms of moment equations. The Langevin approximation is analogous concept to the chemical Langevin equation extensively used in chemical reaction kinetics.
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Hauptvortrag / Eingeladener Vortrag auf einer Tagung