In home range studies, statistical analysis of radio telemetry data poses special problems due to lack of independence of successive observations along the sample path. Assuming that such data are generated by a continuous, stationary, Gaussian process possessing the Markov property, then a multivariate Ornstein-Uhlenbeck diffusion process is necessarily the source and is proposed here to be a workable model. Its characterization is given in terms of typical descriptive properties of home range such as center of activity and confidence regions. Invariance of the model with respect to choice of an observational coordinate system is established, while data for twin deer are used to illustrate the manner in which the model may be used for study of territorial interaction. An approximate maximum likelihood procedure is proposed with results being reported for deer, coyote and bird tracking data.