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

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  • 1Department of Mathematics "G. Peano", University of Torino,Via Carlo Alberto 10, 10123 Turin, Italy.

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|November 9, 2019
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Summary

This study numerically solves the Inverse First Passage time problem for a 2D Gauss-Markov diffusion process. It explores boundary shapes for Inverse Gaussian and Gamma distributions, with neuroscience applications.

Keywords:
GammaInverse First-passage-time problemInverse Gaussiantwo-compartment leaky integrate and fire modeltwo-dimensional Ornstein Uhlenbeck process

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Area of Science:

  • Stochastic processes
  • Computational mathematics
  • Mathematical physics

Background:

  • The Inverse First Passage time problem is crucial for understanding stochastic processes.
  • It involves determining a boundary from a process and a first passage time distribution.
  • Gauss-Markov diffusion processes are widely used in modeling complex systems.

Purpose of the Study:

  • To numerically solve the Inverse First Passage time problem for a two-dimensional Gauss-Markov diffusion process.
  • To investigate how boundary shapes vary with different first passage time distributions (Inverse Gaussian, Gamma).
  • To explore the impact of parameter choices, including heavy and light tails, on boundary characteristics.

Main Methods:

  • Numerical solution techniques for inverse problems.
  • Analysis of two-dimensional Gauss-Markov diffusion processes.
  • Characterization of boundary shapes for specified probability distributions.

Main Results:

  • The study provides numerical solutions for the Inverse First Passage time problem in the specified context.
  • Identified distinct boundary shapes corresponding to Inverse Gaussian and Gamma distributions.
  • Demonstrated sensitivity of boundary shapes to distribution parameters and tail behaviors.

Conclusions:

  • The numerical approach effectively determines boundaries for the Inverse First Passage time problem.
  • Boundary shapes are significantly influenced by the choice of first passage time distribution and its parameters.
  • Findings have potential applications in neuroscience for modeling neural dynamics.