Unitary processes with independent increments and representations of Hilbert tensor algebras

TL;DR

This paper characterizes unitary increment processes using quantum stochastic integrals on symmetric Fock space and establishes their equivalence to Hudson-Parthasarathy flows under specific conditions.

Contribution

It provides a new representation of unitary increment processes and links them to Hudson-Parthasarathy flows through quantum stochastic calculus.

Findings

Established quantum stochastic integral representation for unitary processes.

Proved unitary equivalence to Hudson-Parthasarathy flows.

Provided conditions under which the equivalence holds.

Abstract

The aim of this article is to characterize unitary increment process by a quantum stochastic integral representation on symmetric Fock space. Under certain assumptions we have proved its unitary equivalence to a Hudson-Parthasarathy flow.