Quantum Stochastic Calculus K.R. PARTHASARATHY

ABSTRACT. The basic integrator processes of quantum stochastic calcu-lus, namely, creation, conservation, and annihilation, are introduced in the Hilbert space of square integrable Brownian functionals. Stochastic integrals with respect to these processes and a quantum Itô's formula are described. As an application two examples of quantum stochastic differential equations are discussed. A continuous time version of Stinespring's theorem on com-pletely positive maps in C*-algebras is exploited to formulate the notion of a quantum Markov process and indicate how classical Markov processes are woven into the fabric of the Schödinger-Heisenberg dynamics of quantum theory. 1