Multiparameter Quantum Stochastic Processes

Abstract

We extend the non-commutative constructions outlined in Ref.1–3 to the general n parameter case, these being integrals over an n - dimensional parameter space, employing martingales as integrand. We extend previous results in type one,1,4 type two1,5 stochastic integrals and introduce new integrals for the Clifford sheet. These stochastic integrals are orthogonal, centred L2 - martingales, obeying isometry properties. We develop the construction to consider general martingale representations for the Clifford sheet.