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In the analysis of Markov chains and processes, it is sometimes convenient toreplace an unbounded state space with a "truncated" bounded state space. Whensuch a replacement is made, one often wants to know whether the equilibriumbehavior of the truncated chain or process is close to that of the untruncatedsystem. For example, such questions arise naturally when considering numericalmethods for computing stationary distributions on unbounded state space. Inthis paper, we use the principle of "regeneration" to show that the stationarydistributions of "fixed state" truncations converge in great generality (intotal variation norm) to the stationary distribution of the untruncated limit,when the untruncated chain is positive Harris recurrent. Even in countablestate space, our theory extends known results by showing that the augmentationcan correspond to an $r$-regular measure. In addition, we extend our theory tocover an important subclass of Harris recurrent Markov processes that includenon-explosive Markov jump processes on countable state space.

On Convergence of a Truncation Scheme for Approximating Stationary Distributions of Continuous State Space Markov Chains and Processes