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Math Biosci Eng. 2019 Sep 10;16(6):8162-8178. doi: 10.3934/mbe.2019412.

The Inverse First Passage time method for a two dimensional Ornstein Uhlenbeck process with neuronal application.

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Department of Mathematics "G. Peano", University of Torino,Via Carlo Alberto 10, 10123 Turin, Italy.


The Inverse First Passage time problem seeks to determine the boundary corresponding to a given stochastic process and a fixed first passage time distribution. Here, we determine the numerical solution of this problem in the case of a two dimensional Gauss-Markov diffusion process. We investigate the boundary shape corresponding to Inverse Gaussian or Gamma first passage time distributions for different choices of the parameters, including heavy and light tails instances. Applications in neuroscience framework are illustrated.


Gamma ; Inverse First-passage-time problem ; Inverse Gaussian ; two-compartment leaky integrate and fire model ; two-dimensional Ornstein Uhlenbeck process

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