Expansions of Iterated Stratonovich Stochastic Integrals from the Taylor-Stratonovich Expansion, Based on Multiple Trigonometric Fourier Series. Comparison With the Milstein Expansion

TL;DR

This paper compares two methods for expanding iterated Stratonovich stochastic integrals: the Milstein expansion and a Fourier series-based approach, analyzing their effectiveness and practical applications.

Contribution

It introduces a comparison between the Milstein expansion and a Fourier series-based expansion for iterated Stratonovich stochastic integrals, highlighting their relative effectiveness.

Findings

Fourier series expansions are effective for iterated stochastic integrals.

Comparison shows differences in efficiency between Fourier-Legendre and trigonometric series.

Practical implications for stochastic calculus applications are discussed.

Abstract

The article is devoted to comparison of the Milstein expansion of iterated Stratonovich stochastic integrals with the method of expansion of iterated stochastic integrals based on generalized multiple Fourier series. We consider some practical material connected with the expansions of iterated Stratonovich stochastic integrals from the Taylor-Stratonovich expansion based on multiple trigonometric Fourier series. The comparison of effectiveness of the Fourier-Legendre series as well as the trigonomertic Fourier series for expansion of iterated Stratonovich stochastic integrals is considered.