Gibbs states on the symbolic space over an infinite alphabet

We consider subshifts of finite type on the symbolic space generated by inc idence matrices over a countably infinite alphabet. We extend the definitio n of topological pressure to this context and, as our main result, we const ruct a new class of Gibbs states of Holder continuous potentials on these s ymbol spaces. We establish some basic stochastic properties of these Gibbs states: exponential decay of correlations, central limit theorem and an a.s . invariance principle. This is accomplished via detailed studies of the as sociated Perron-Frobenius operator and its conjugate operator.