Properties of Hida processes on 2. 2. Prediction and interpolation problems for processes on 2

The properties of N-Hida processes Part 1 ([6.], J. Multivar. Anal. 15, 336-360) are studied when the indices set is 2. First, the past of a point (s, t) of 2 is extended to st = [sigma]{[gamma]uv, u <= s or v <= t}. The dimension of the linear space generated by the conditional expectations of an N-Hida process [gamma]z when z goes over a p - q lattice is bounded by N(p + q - 1). The same problem is then considered when the expectations are taken conditionally to the field generated by the process outside of a rectangle, and the bound of the dimension of the linear space generated on a lattice is also given. Special attention is devoted to the case when [gamma]z is a combination of strong martingales.