# The dyadic fractional diffusion kernel as a central limit

## TL;DR

This paper derives the fundamental solution for dyadic diffusions on the positive real line using Haar wavelet analysis, showing it as a central limit of mollified stable Markov kernels.

## Contribution

It introduces a novel approach replacing Fourier analysis with Haar wavelet analysis to analyze dyadic diffusions and their fundamental solutions.

## Key findings

- Fundamental solution kernel obtained via dyadic mollification.
- Haar wavelet analysis effectively replaces Fourier analysis.
- Central limit theorem established for dyadic diffusions.

## Abstract

In this paper we obtain the fundamental solution kernel of dyadic diffusions in $\mathbb{R}^+$ as a Central Limit of dyadic mollification of iterations of stable Markov kernels. The main tool is provided by the substitution of classical Fourier analysis by Haar wavelet analysis.