# The Inverse first passage time method for a two dimensional Ornstein Uhlenbeck process with neuronal application

## TL;DR

This paper develops a numerical method to solve the inverse first passage time problem for a two-dimensional Ornstein-Uhlenbeck process, with applications in neuroscience, exploring boundary shapes for various distributions.

## Contribution

It introduces a numerical solution for the inverse first passage time problem in 2D Gauss-Markov processes, with novel applications to neuronal modeling.

## Key findings

- Boundary shapes vary with different first passage time distributions.
- The method handles heavy and light tail distributions effectively.
- Applications demonstrate relevance to neuroscience modeling.

## 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.