# Revisiting Feller Diffusion: Derivation and Simulation

## TL;DR

This paper presents a simplified derivation of the Feller Diffusion's probability density function using Fourier Transform and Characteristics, along with simulation algorithms to verify hitting time properties.

## Contribution

It introduces a more straightforward derivation method and discusses simulation techniques for Feller Diffusion, enhancing understanding and computational approaches.

## Key findings

- Derived the Feller Diffusion PDF using Fourier Transform and Characteristics.
- Validated hitting time properties through simulation.
- Provided practical algorithms for simulating Feller Diffusion.

## Abstract

We propose a simpler derivation of the probability density function of Feller Diffusion using the Fourier Transform and solving the resulting equation via the Method of Characteristics. We also discuss simulation algorithms and confirm key properties related to hitting time probabilities via the simulation.