  Following an approach presented by N. Frantzikinakis, we prove that any
multiple correlation sequence, defined by invertible measure preserving actions
of commuting transformations with integer part polynomial iterates, is the sum
of a nilsequence and an error term, small in uniform density. As an
intermediate result, we show that multiple ergodic averages with iterates given
by the integer part of real valued polynomials converge in the mean. Also, we
show that under certain assumptions the limit is zero. An important role in our
arguments plays a transference principle, communicated to us by M. Wierdl, that
enables to deduce results for $\mathbb{Z}$-actions from results for flows.
