Stochastic Integration in Banach Spaces using a product structure with partial order

TL;DR

This paper introduces a novel weak Banach space-valued stochastic integral leveraging a multiplicative structure and partial order, expanding the tools for stochastic analysis in Banach spaces.

Contribution

It constructs a weak stochastic integral in Banach spaces using a product structure and partial order, a new approach in the field.

Findings

Defines a weak stochastic integral in Banach spaces.

Utilizes multiplicative structures like Banach algebras.

Provides a framework for stochastic integration with square integrable martingales.

Abstract

Using a multiplicative structure (for example that of a Banach algebra) and a partial order we construct a weak version of a Banach space valued stochastic integral with respect to square integrable martingales.