Propagation of Chaos for Stochastic Spatially Structured Neuronal Networks with Delay driven by Jump Diffusions

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.

arXiv commentIn this version, a shorter title has been chosen. The manuscript has been accepted for publication in Annals of Applied Probability

References in corpus (4)

• Propagation of chaos in neural fields
• Mean field limit for disordered diffusions with singular interactions
• Limits and dynamics of stochastic neuronal networks with random heterogeneous delays
• Spatially extended networks with singular multi-scale connectivity patterns

Cited by in corpus (7)

• On Explicit Milstein-type Scheme for Mckean-Vlasov Stochastic Differential Equations with Super-linear Drift Coefficient
• Well-posedness and tamed Euler schemes for McKean-Vlasov equations driven by Lévy noise
• Exponential ergodicity for SDEs and McKean-Vlasov processes with Lévy noise
• Large deviations for interacting diffusions with path-dependent McKean-Vlasov limit
• Delay-induced periodic behavior in competitive populations
• On pathwise uniqueness for multidimensional McKean--Vlasov equations
• A Stochastic Gronwall Lemma and Well-Posedness of Path-Dependent SDEs Driven by Martingale Noise