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This article provides a survey of approximation metrics for stochastic processes. We deal with Markovian processes in discrete time evolving on general state spaces, namely on domains with infinite cardinality and endowed with proper measurability and metric structures. The focus of this work is to discuss approximation metrics between two such processes, based on the notion of probabilistic bisimulation: in particular we investigate metrics characterized by an approximate variant of thisdoi:10.1016/j.entcs.2013.12.002 fatcat:bda7mwwxzvarti2ok7wgrrkyt4