Projection of processes with orthogonal increments and subordinated processes

Second-order random processes are considered as curves in a Hilbert space $\mathscr H$ of random variables $\xi$ with $E_\xi=0$, $E|\xi|^2<\infty$. Processes which are a projection of a given process $x(t)$ with orthogonal increments on some subspaces of $\mathscr H$ are considered. Processes subordinate to $x(t)$ are also considered.