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

  • Received: 12 March 2019 Accepted: 03 June 2019 Published: 10 September 2019
  • 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.

    Citation: Alessia Civallero, Cristina Zucca. The Inverse First Passage time method for a two dimensional Ornstein Uhlenbeck process with neuronal application[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 8162-8178. doi: 10.3934/mbe.2019412

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  • 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.




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    6. Graziano Crasta, Virginia De Cicco, Guido De Philippis, Kinetic Formulation and Uniqueness for Scalar Conservation Laws with Discontinuous Flux, 2015, 40, 0360-5302, 694, 10.1080/03605302.2014.979998
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