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In structural character recognition, a character is usually viewed as a set of strokes and the spatial relationships between them. Therefore, strokes and their relationships should be properly modeled for effective character representation. For this purpose, we propose a modeling scheme by which strokes as well as relationships are stochastically represented by utilizing the hierarchical characteristics of target characters. A character is defined by a multivariate random variable over the components and its probability distribution is learned from a training data set. To overcome difficulties of the learning due to the high order of the probability distribution (a problem of curse of dimensionality), the probability distribution is factorized and approximated by a set of lower-order probability distributions by applying the idea of relationship decomposition recursively to components and subcomponents. Based on the proposed method, a handwritten Hangul (Korean) character recognition system is developed. Recognition experiments conducted on a public database show the effectiveness of the proposed relationship modeling. The recognition accuracy increased by 5.5 percent in comparison to the most successful system ever reported.