On the orthogonal expansion of iterated Stratonovich stochastic integrals

TL;DR

This paper investigates the orthogonal expansion of iterated Stratonovich stochastic integrals, establishing a relationship between the expansion coefficients and the integral trace for certain function classes.

Contribution

It introduces a framework for representing iterated Stratonovich integrals via orthogonal expansions and proves the equality of coefficient trace and integral trace for specific functions.

Findings

Established the orthogonal expansion for a class of functions

Proved the equality of expansion coefficient trace and integral trace

Provided a theoretical foundation for stochastic integral approximation

Abstract

We consider a class of functions for which the multiple Stratonovich stochastic integral or equivalent iterated Stratonovich stochastic integral with square integrable weights is defined by the orthogonal expansion. The equality of the trace of expansion coefficients matrix for these functions and the corresponding integral trace is established.