Quantum Stochastic Calculus
Quantum stochastic calculus is a differential calculus for the bewildering variety of noises in quantum world. The first quantum stochastic calculus was introduced by R. L. Hudson and K. R. Parthasarathy for Bose noises. Roughly speaking, this is a sort of Ito calculus for the most fundamental noises in quantum theory. The study of stochastic calculi for several types of noises (Bose, Fermi, free, Boolean, monotonic, ...) is still a hot topic.
Quantum stochastic differential equations are stochastic differential equations for operator processes driven by quantum noises. They are applied in the study of the evolution of quantum open systems, in the theory of quantum continual measurements, in the study of quantum Markov processes and dilations of quantum Markov semigroups [Fa03a, FW03, Gr00, Gr01, Gr05a, Gr05b, Ba06a, BC11, G15].