  The nuclear medium effects in the nuclear structure functions and
differential cross sections in the deep inelastic scattering (DIS) of charged
lepton and neutrino from nuclear targets are studied in the region of large $x$
including $x\ge 1$. The nuclear medium effects due to the Fermi motion and the
binding energy of nucleons and the nucleon correlations are included using
nucleon spectral function calculated in a microscopic field theoretical model.
The numerical results for the nuclear structure functions and the cross
sections are obtained using the nucleon structure function evaluated at the
next-to-next-to-leading order (NNLO) with the Martin-Motylinski-Harland
Lang-Thorne (MMHT) parameterization of the nucleonic parton distribution
functions (PDFs) and are compared with the available experimental data on
electron scattering from the Jefferson Lab (JLab) and SLAC Nuclear Physics
Facility (NPAS). In the case of neutrino scattering the results are relevant
for understanding the DIS contributions to the recent inclusive cross sections
measured by the Main Injector Neutrino ExpeRiment to study v-A interactions
(MINERvA) as well as theoretical predictions are made for Deep Underground
Neutrino Experiment (DUNE). The importance of isoscalarity corrections in
heavier nuclear targets as well as the effect of the kinematic cut on the CM
energy $W$ in defining the DIS region have also been discussed.
