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In this paper, we discuss how to check Probablistic Computation Tree Logic (PCTL) logic operators over infinite state Discrete Time Markov Chains (DTMC). Probabilistic model checking has been largely applied over finite state space Markov models. Recently infinite state models have been considered when underlying infinite Markov models have special structures. We propose to consider finite state models providing bounds on transient and the stationary distributions in the sense of the $\preceq_{st}$ stochastic order to check infinite state models. The operators of the PCTL logic are then checked by considering these finite bounding models.