By abstracting the multiplication rule for ℤ₂-graded quantum stochastic integrals, we construct a ℤ₂-graded version of the Itô Hopf algebra, based on the space of tensors over a ℤ₂-graded associative algebra. Grouplike elements of the corresponding algebra of formal power series are characterised.
The coefficients of the moments of the monotone Poisson law are shown to be a type of Stirling number of the first kind; certain combinatorial identities relating to these numbers are proved and a new derivation of the Cauchy transform of this law is given. An investigation is begun into the classical Azéma-type martingale which corresponds to the compensated monotone Poisson process; it is shown to have the chaotic-representation property and its sample paths are described.