Before revision:  A necessary and sufficient condition for integration of order d=1,2,\dots is given in terms of the decomposition of the space H into the direct sum of d+1 closed subspaces \tau_h, h=0, , d, each one associated with components of the process integrated of order h.
After revision:  A necessary and sufficient condition for integration of order d=1,2,\dots  , d, each one associated with components of the process integrated of order h.