Approximating functions on stratified sets

TL;DR

This paper develops methods for smooth function approximation on stratified sets with specific gradient conditions, and explores implications for matrix-valued Bessel processes.

Contribution

It introduces new approximation techniques tailored for stratified sets and connects these to properties of matrix-valued Bessel processes.

Findings

Successful approximation of functions with prescribed gradients on stratified sets

Implications for the behavior of matrix-valued Bessel processes

Potential applications in stochastic analysis and geometric measure theory

Abstract

We investigate smooth approximations of functions, with prescribed gradient behavior on a distinguished stratified subset of the domain. As an application, we outline how our results yield important consequences for a recently introduced class of stochastic processes, called the matrix-valued Bessel processes.