Propagation of chaos for stochastic spatially structured neuronal networks with delay driven by jump diffusions
Sima Mehri, Michael Scheutzow, Wilhelm Stannat, Bian Z. Zangeneh
Abstract
Spatially structured neural networks driven by jump diffusion noise with monotone coefficients, fully path dependent delay and with a disorder parameter are considered. Well-posedness for the associated McKean–Vlasov equation and a corresponding propagation of chaos result in the infinite population limit are proven. Our existence result for the McKean–Vlasov equation is based on the Euler approximation that is applied to this type of equation for the first time.
Topics & Concepts
JumpLimit (mathematics)Monotone polygonMathematicsDiffusionStatistical physicsPopulationApplied mathematicsPath (computing)Mathematical analysisPhysicsComputer scienceDemographyGeometryQuantum mechanicsThermodynamicsSociologyProgramming languagestochastic dynamics and bifurcationNeural Networks Stability and SynchronizationAdvanced Thermodynamics and Statistical Mechanics