Weak convergence of marked point processes generated by crossings of multivariate jump processes. applications to neural network modeling

DOI10.1016/j.physd.2014.08.003zbMath1360.60097arXiv1310.6933OpenAlexW1993353318MaRDI QIDQ528850

Martin Jacobsen, Massimiliano Tamborrino, Laura Sacerdote

Publication date: 17 May 2017

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.6933

zbMATH Keywords

neural networkfirst passage timeweak and strong convergencediffusion limitKurtz approximationmultivariate diffusion process

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Diffusion processes (60J60) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (8)

A new firing paradigm for integrate and fire stochastic neuronal models ⋮ The Jacobi diffusion process as a neuronal model ⋮ Asymptotic results for weighted means of linear combinations of independent Poisson random variables ⋮ First passage times of two-dimensional correlated processes: analytical results for the Wiener process and a numerical method for diffusion processes ⋮ Jacobi Processes with Jumps as Neuronal Models: A First Passage Time Analysis ⋮ Shot noise, weak convergence and diffusion approximations ⋮ Input-output consistency in integrate and fire interconnected neurons ⋮ Restricted Ornstein-Uhlenbeck process and applications in neuronal models with periodic input signals

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