On two approaches for obtain of the generalized Ito-Wentzell formula

TL;DR

This paper compares two methods for deriving the generalized Ito-Wentzell formula, one using generalized Ito's formula and the other based on kernel functions for integral invariants.

Contribution

It introduces and analyzes two distinct approaches for deriving the generalized Ito-Wentzell formula, highlighting their theoretical foundations and differences.

Findings

Both approaches successfully derive the generalized Ito-Wentzell formula.

The kernel functions method offers a new perspective on integral invariants.

The paper discusses the advantages and limitations of each approach.

Abstract

We consider two approaches for obtain of the generalized Ito-Wentzell formula: the first way uses the generalized Ito's formula; the second one is based on a concept of kernel functions for integral invariants.