In this paper, we study unitary Gaussian processes with independent increments with which the unitary equivalence to a Hudson-Parthasarathy evolution systems is proved. This gives a generalization of results in [16] and [17] in the absence of the stationarity condition.
This is a continuation of the earlier work cite{SSS} to characterize stationary unitary increment Gaussian processes. The earlier assumption of uniform continuity is replaced by weak continuity and with a technical assumption on the domain of the gen
erator, unitary equivalence of the processes to the solution of Hudson-Parthasarathy equation is proved.
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.
