  Point processes are finding growing applications in numerous fields, such as
neuroscience, high frequency finance and social media. So classic problems of
classification and clustering are of increasing interest. However, analytic
study of misclassification error probability in multi-class classification has
barely begun. In this paper, we tackle the multi-class likelihood
classification problem for point processes and develop, for the first time,
both asymptotic upper and lower bounds on the error rate in terms of computable
pair-wise affinities. We apply these general results to classifying renewal
processes. Under some technical conditions, we show that the bounds have
exponential decay and give explicit associated constants. The results are
illustrated with a non-trivial simulation.
