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

Alessia Civallero; Cristina Zucca; Alessia Civallero; Cristina Zucca

doi:10.3934/mbe.2019412

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 8162-8178. doi: 10.3934/mbe.2019412

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

Alessia Civallero ,
Cristina Zucca ^,

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

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

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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