Continuous authentication (CA) with touch stroke dynamics is an emerging problem for mobile identity management. In this paper, we focus on one of the essential problems in CA namely one-class classification problem. We propose a novel analytic probabilistic one-class classifier coined One-Class Random MaxOut Probabilistic Network (OC-RMPNet). The OC-RMPNet is a single hidden layer network that is tailored to capture individual users' touch-stroke profiles. The input-hidden layer of the network is meant to project the input vector onto the high dimensional random maxout feature space and the hidden-output layer acts as an OC probabilistic predictor that trained by means of least-square principle, hence require no iterative learning. We also put forward a feature sequential fusion mechanism for accuracy improvement. We scrutinize and compare the proposed methods with existing works on touchanalytics and HMOG datasets. The empirical results reveal that the OC-RMPNet prevails over its predecessor in touch-stroke authentication tasks on mobile phones.