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.
Highlights
IntroductionIn many situations arising from applications (i.e. neuroscience, finance, reliability, ...), the quantity of interest is the first time that a random quantity crosses a given fixed level
In many situations arising from applications, the quantity of interest is the first time that a random quantity crosses a given fixed level
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
Summary
In many situations arising from applications (i.e. neuroscience, finance, reliability, ...), the quantity of interest is the first time that a random quantity crosses a given fixed level. It can happen that the FPT distribution is known as well as the random process, while one is interested in determining the corresponding time dependent boundary. This is the so-called Inverse FPT problem. The same framework is in [4], where possible thresholds corresponding to Gamma distributed FPTs for an OU process has been investigated with modelling purposes.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
