The stationary analysis of continuous-time Markov chains (CTMCs) on countably infinite state spaces is a cornerstone of applied probability, but the direct computation of the stationary measure \(\varvec{\pi }\) is often intractable. A standard remedy is the augmented truncation method, which approximates \(\varvec{\pi }\) by the stationary measure \(\tilde{\varvec{\pi }}^{(k)}\) of a finite-state process. While convergence of \(\tilde{\varvec{\pi }}^{(k)}\) to \(\varvec{\pi }\) is known in certain cases, the central challenge for practical applications lies in obtaining computable, a priori error bounds. A key contribution is a simple truncation/augmentation construction that renders the truncated states transient, thereby enabling a particularly tractable finite-row perturbation structure. This paper applies the perturbation theory of Markov chains to the problem of augmented truncation to derive explicit error bounds on the V-norm distance \(\Vert \tilde{\varvec{\pi }}^{(k)}- \varvec{\pi }\Vert _{\textbf{V}}\) . Using the deviation matrix \(\textbf{D}\) of the original process, we first establish an exact identity linking the approximation error to the perturbation operator \(\varvec{\Delta }^{(k)}\) , \(\tilde{\varvec{\pi }}^{(k)}- \varvec{\pi }= \tilde{\varvec{\pi }}^{(k)}\varvec{\Delta }^{(k)}\textbf{D}\) . We then decompose this identity into two interpretable and computable components: a “tail term” that depends on the original process dynamics outside the truncated state space, and an “augmentation term” controlled by the redistribution policy of the lost probability mass. We prove that this decomposition holds for any arbitrary augmentation scheme and show that the error bound can be minimized by an optimal choice of this policy, which we explicitly characterize. The resulting bounds are particularly powerful as they do not require strong structural assumptions like stochastic monotonicity. The methodology is illustrated on a non-trivial M/M/1 retrial queue, demonstrating its applicability and the behavior of the computable components of the bound.
