Smooth approximations for fractional and multifractional fields

TL;DR

This paper introduces smooth stochastic processes that approximate complex fractional and multifractional Brownian sheets, enabling better analysis and simulation of these fields in mathematical and applied contexts.

Contribution

It develops a method to construct absolutely continuous processes converging to anisotropic fractional and multifractional Brownian sheets in Besov spaces.

Findings

Successfully approximates fractional fields with smooth processes

Provides convergence results in Besov-type spaces

Enhances tools for analyzing complex stochastic fields

Abstract

We construct absolute continuous stochastic processes that converge to anisotropic fractional and multifractional Brownian sheets in Besov-type spaces.