Quantum stochastic processes with independent additive increments

AbstractWe give a complete characterization of a class of quantum stochastic processes with independent, stationary increments. We prove that processes of the class are, up to a canonical equivalence, equal to a sum of creation, second quantization, annihilation, and scalar processes on a Bose/Fermi Fock space, showing that, with our notion of independence, there are no other “white noises” but those used in the quantum stochastic calculus of R. L. Hudson and K. R. Parthasarathy