Stochastic spike arrival as an important source of noise has been discussed by Stein in the context of integrate-and-fire models (494; 495). The accessible review article of Konig et al. (273) highlights how stochastic spike arrival in the input can lead to a broad interspike interval distribution in the output of a neuron. The close relation between stochastic spike arrival and diffusive noise has been known for a long time (190; 243). The leaky integrate-and-fire model with diffusive noise is equivalent to the Ornstein-Uhlenbeck process (527) with an absorbing boundary. Mathematical results for integrate-and-fire models with diffusive noise are reviewed in Tuckwell (526). A in-depth treatment of the mathematical theory of stochastic processes and Fokker-Planck equations can be found in van Kampen (529).
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