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Propagation of chaos for stochastic spatially structured neuronal networks with delay driven by jump diffusions

Mehri, S ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1214/19-AAP1499
  3. Publisher: Institute of Mathematical Statistics , 2020
  4. Abstract:
  5. 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. © 2020 Institute of Mathematical Statistics
  6. Keywords:
  7. Fully path dependent delay ; McKean-Vlasov equations ; Mean-field limits ; Monotone coefficients ; Propagation of chaos ; Spatially structured neural networks
  8. Source: Annals of Applied Probability ; Volume 30, Issue 1 , February , 2020 , Pages 175-207
  9. URL: https://projecteuclid.org/journals/annals-of-applied-probability/volume-30/issue-1/Propagation-of-chaos-for-stochastic-spatially-structured-neuronal-networks-with/10.1214/19-AAP1499.short