Bimeasures and measures induced by planar Stochastic integrators

Two parameter Stochastic processes {Xz([omega]), [omega] [set membership, variant] [Omega], z [set membership, variant] +2} which are L2 integrators are characterized through associated bimeasures defined on the product spaces ([Omega] - +2) - ([Omega] - +2) and and [Omega] - +2 - +2. It is also shown that under further restrictions on the X process there exists an associated measure on these product spaces and Xz2 possesses a Doob-Meyer-Cairoli decomposition.