Localization of Wiener Functionals of Fractional Regularity and Applications

TL;DR

This paper refines the localization of fractional Wiener functionals, providing precise estimates for differences in Donsker's delta functionals and applying these results to analyze the convergence rate of Euler scheme densities for non-Markovian SDEs.

Contribution

It advances the understanding of fractional Wiener functionals by localizing Watanabe's results and applying them to convergence analysis of stochastic differential equations.

Findings

Precise estimates for differences between fractional Donsker's delta functionals.

Convergence rate results for Euler scheme densities of non-Markovian SDEs.

Extension of localization techniques to fractional Wiener functionals.

Abstract

In this paper we localize some of Watanabe's results on fractional Wiener functionals, and use them to give a precise estimate of the difference between two Donsker's delta functionals even with fractional differentiability. As an application, the convergence rate of the density of the Euler scheme for non-Markovian stochastic differential equations is obtained.