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In this paper, we present a modified hidden Markov model with emission probabilities modelled by kernel density estimation and its use for activity recognition in videos. In the proposed approach, kernel density estimation of the emission probabilities is operated simultaneously with that of all the other model parameters by an adapted Baum-Welch algorithm. This allows us to retain maximum-likelihood estimation while overcoming the known limitations of mixture of Gaussians in modelling certain probability distributions. Experiments on activity recognition have been performed on ground-truthed data from the CAVIAR video surveillance database and reported in the paper. The error on the training and validation sets with kernel density estimation remains around 14-16% while for the conventional Gaussian mixture approach varies between 15 and 24%, strongly depending on the initial values chosen for the parameters. Overall, kernel density estimation proves capable of providing more flexible modelling of the emission probabilities and, unlike Gaussian mixtures, does not suffer from being highly parametric and of difficult initialisation.