Rocking responses of rigid objects under combined deterministic and st
ochastic excitations of arbitrary relative intensities are examined fr
om a fully probabilistic perspective. The associated Fokker-Planck equ
ation is derived and numerically solved by a path-integral solution pr
ocedure to obtain the joint probability density functions (JPDFs). The
evolutions and the steady states of the JPDFs are employed to elucida
te the global behaviour of the rocking responses. As found in the comp
anion paper, numerical results confirm that the presence of stochastic
excitation bridges the domains of attraction of coexisting responses,
and that overturning attractors are of the greatest relative stabilit
y. Thus, all rocking response trajectories that visit near the heteroc
linic orbit will eventually lead to overturning under the influence of
stochastic excitation. A rapid leakage of the probability (mass) out
of the ''safe'' (bounded, chaotic) domain to the overturning regime im
plies weak stability of the chaotic attractor. Using mean first-passag
e time as a performance index, sensitivity of rocking responses to sys
tem parameters and (non)stationarity of the stochastic excitation is a
lso investigated.