QUANTUM AND NONCAUSAL STOCHASTIC CALCULUS

The quantum stochastic calculus initiated by Hudson and Parthasarathy, and the non-causal stochastic calculus originating with the papers of Hitsuda and Skorohod, are two potent extensions of the Ito calculus, currently enjoying intensive development. The former provides a quantu m probabilistic extension of Schrodinger's equation, enabling the cons truction of a Markov process for a quantum dynamical semigroup. The la tter allows the treatment of stochastic differential equations which i nvolve terms which anticipate the future. In this paper the close rela tionship between these theories is displayed, and a non-causal quantum stochastic calculus, already in demand from physics, is described.