Conjugate operators to operators of stochastic integration

TL;DR

This paper investigates conjugate operators related to stochastic integration, focusing on their properties when acting on spaces of progressively measurable random functions, advancing the mathematical framework of stochastic optimal control.

Contribution

It introduces and analyzes specific conjugate operators to stochastic integration operators on spaces of progressively measurable functions, expanding theoretical understanding.

Findings

Characterization of conjugate operators in stochastic integration

Insights into operator behavior on measurable function spaces

Potential applications in stochastic control theory

Abstract

The conjugate problem in stochastic optimal control can be formulated in terms of operators conjugated to the operators of stochastic integration [1, 2, 3]. In this paper we study some of such operators acting on the spaces of progressively measurable random functions.