On the the successive passage times of certain one-dimensional diffusions

TL;DR

This paper investigates the distribution of the nth-passage time for certain one-dimensional diffusions derived from Brownian motion via transformations, providing detailed results and explicit examples.

Contribution

It extends previous work on Brownian motion to a broader class of diffusions, detailing their passage time distributions with explicit examples.

Findings

Derived explicit formulas for passage time distributions

Extended results from Brownian motion to transformed diffusions

Provided detailed examples illustrating the theoretical results

Abstract

We show in detail some results, outlined in a previous paper regarding the case of Brownian motion (BM), about the distribution of the $n$th-passage time of a one-dimensional diffusion obtained by a space or time transformation of BM, through a constant barrier $a.$ Some explicit examples are reported.