  We construct matrix product steady state for a class of interacting particle
systems where particles do not obey hardcore exclusion, meaning each site can
occupy any number of particles subjected to the global conservation of total
number of particles in the system. To represent the arbitrary occupancy of the
sites, the matrix product ansatz here requires an infinite set of matrices
which in turn leads to an algebra involving infinite number of matrix
equations. We show that these matrix equations, in fact, can be reduced to a
single functional relation when the matrices are parametric functions of the
representative occupation number. We demonstrate this matrix formulation in a
class of stochastic particle hopping processes on a one dimensional periodic
lattice where hop rates depend on the occupation numbers of the departure site
and its neighbors within a finite range; this includes some well known
stochastic processes like, totally asymmetric zero range process, misanthrope
process, finite range process and partially asymmetric versions of the same
processes but with different rate functions depending on the direction of
motion.
