  This work examines a class of switching jump diffusion processes. The main
effort is devoted to proving the maximum principle and obtaining the Harnack
inequalities. Compared with the diffusions and switching diffusions, the
associated operators for switching jump diffusions are non-local, resulting in
more difficulty in treating such systems. Our study is carried out by taking
into consideration of the interplay of stochastic processes and the associated
systems of integro-differential equations.
