Quantum stochastic processes with independent additive increments

C. Barnett, R. F. Streater, Ivan F. Wilde

Peter Glockner

Many examples of quantum independent stationary increment processes are solutions of quantum stochastic differential equations. We give a common characterization of these examples by a quantum stochastic differential equation on an abstract *-bialgebra. Specializing this abstract *-bialgebra and the coefficients of the equation, we obtain the equations for the Unitary Noncommutative Stochastic processes of [12], the Quantum Wiener Process [2], the Azéma martingales [11] and for other examples. The existence and uniqueness of a solution of the general equation is shown. Assuming the boundedness of this solution, we prove that it is a continuous and stationary independent increment process.

Michael Schürmann

Anatolij Dvurečenskij, Sylvia Pulmannová

E. B. Davies

Lingaraj Sahu, Michael Schürmann, Kalyan B. Sinha

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.