The Ito‐Clifford Wong‐Zakai Integrals and Martingale Representation

Classical stochastic integration is based upon a probability space involving a filtration of sigma‐algebras. This construction lends itself to non‐commutative quantum analogues based for example, on a Hilbert space, a filtration of von Neumann algebras and gage. We recall a non‐commutative construction for the two parameter case, these being integrals in the plane, resulting in type one and type two stochastic integrals which are orthogonal, centred L2 — martingales, obeying isometry properties and develop the construction to obtain an Ito‐Clifford Wong‐Zakai martingale representation.