  LIGO and Virgo have initiated the era of gravitational-wave (GW) astronomy;
but in order to fully explore GW frequency spectrum, we must turn our attention
to innovative techniques for GW detection. One such approach is to use binary
systems as dynamical GW detectors by studying the subtle perturbations to their
orbits caused by impinging GWs. We present a powerful new formalism for
calculating the orbital evolution of a generic binary coupled to a stochastic
background of GWs, deriving from first principles a secularly-averaged
Fokker-Planck equation which fully characterises the statistical evolution of
all six of the binary's orbital elements. We also develop practical tools for
numerically integrating this equation, and derive the necessary statistical
formalism to search for GWs in observational data from binary pulsars and
laser-ranging experiments.
