  A powerful statistical interpolating concept, which we call \emph{fully
lifted} (fl), is introduced and presented while establishing a connection
between bilinearly indexed random processes and their corresponding fully
decoupled (linearly indexed) comparative alternatives. Despite on occasion very
involved technical considerations, the final interpolating forms and their
underlying relations admit rather elegant expressions that provide conceivably
highly desirable and useful tool for further studying various different aspects
of random processes and their applications. We also discuss the generality of
the considered models and show that they encompass many well known random
structures and optimization problems to which then the obtained results
automatically apply.
