We present a novel statistical paradigm for modeling and analysis of gait variability which captures the natural point process structure of gait intervals and allows for definition of new measures instantaneous mean and standard deviation. We validate our model using two existing data sets from physionet.org. Results show an excellent model fit and yield insights into the underlying statistical structure behind human gait. Statistical analyses further corroborate previous findings of increased variability in gait at different speeds, both self-paced and metronome-paced, and reveal a significant increase in gait variability in Parkinson's subjects, as compared to young and elderly healthy subjects. These results indicate the validity of a point process approach to the analysis of gait, and the potential utility of incorporating instantaneous measures of gait into diagnostic or patient monitoring applications.