Stochastic integral representations of quantum martingales on multiple Fock space

TL;DR

This paper develops a quantum stochastic integral representation theorem for unbounded regular martingales in multidimensional quantum noise, extending previous results to more general settings.

Contribution

It introduces a new integral representation theorem for unbounded quantum martingales in multidimensional Fock spaces, broadening the scope of prior work.

Findings

Extended Parthasarathy and Sinha's results to unbounded martingales.

Generalized the integral representation to multidimensional quantum noise.

Provided a framework for analyzing unbounded quantum martingales.

Abstract

In this paper a quantum stochastic integral representation theorem is obtained for unbounded regular martingales with respect to multidimensional quantum noise. This simultaneously extends results of Parthasarathy and Sinha to unbounded martingales and those of the author to multidimensions.