"The direct approach" for a proof of the generalized Ito-Wentzell formula for a generalized stochastic differential equation

TL;DR

This paper provides a complete proof of a method to derive the generalized Ito-Wentzell formula for stochastic differential equations, utilizing Ito's formula and stochastic approximation theory, building on earlier preliminary ideas.

Contribution

It introduces a rigorous proof of the generalized Ito-Wentzell formula using a novel approach based on Ito's formula and stochastic approximation theory.

Findings

Complete proof of the generalized Ito-Wentzell formula

Method based on Ito formula and stochastic approximation

Clarifies the approach announced earlier

Abstract

This paper is complete proof of one method for obtaining the generalized Ito-Wentzell formula, its basic idea was announced earlier in a pre-print (arXiv:1309.3038v1). This proof sets the approach which uses the Ito formula and the stochastic approximation theory.