We present a framework for the classification of visual processes that are best modeled with spatio-temporal autoregressive models. The new framework combines the modeling power of a family of models known as dynamic textures and the generalization guarantees, for classification, of the support vector machine classifier. This combination is achieved by the derivation of a new probabilistic kernel based on the Kullback-Leibier divergence (KL) between Gauss-Markov processes. In particular, we derive the KL-kernel for dynamic textures in both 1) the image space, which describes both the motion and appearance components of the spatio-temporal process, and 2) the hidden state space, which describes the temporal component alone. Together, the two kernels cover a large variety of video classification problems, including the cases where classes can differ in both appearance and motion and the cases where appearance is similar for all classes and only motion is discriminant. Experimental evaluation on two databases shows that the new classifier achieves superior performance over existing solutions.