Quantum stochastic integration and quantum stochastic differential equations
Chris Barnett, Stanisław Goldstein, Ivan F. Wilde
Abstract Quantum stochastic integrals are constructed using the non-commutative L p -space theory of Haagerup. The existence and uniqueness of the solution to quantum stochastic differential equations driven by quasi-Wiener noises, or noises satisfying generalized standing hypotheses, is established as is the Markov behaviour of the solution. Various examples of the theory are discussed, and quantum Ornstein-Uhlenbeck processes are obtained as explicit solutions.
Mathematical Proceedings of the Cambridge Philosophical Society•Nov 1, 1994•6 citations