Electricity theft can range up to 40% of the total electricity distributed in some countries. Improving the detection of electricity theft with novel models thrives significant economic value by allowing electricity providers to generate more revenue and to increase the stability of their electricity grid. The novelty of this project is to push the frontiers of modeling electricity theft through stochastic processes. Certain neighborhoods are more likely to steal electricity than others. We therefore derive features about the neighborhood of customers. Since previous inspections focused on certain neighborhoods, we reduce the sampling bias in the training set using spatial point processes for resampling. Next, we model the temporal dynamics of physical inspects that found fraud using Hawkes processes. Features derived from the neighborhood of the customers and these stochastic processes can then be used in machine learning algorithms to better classify customers into fraudulent and normal. Furthermore, the anomaly detection models created in this project will be generalized and applied to other anomaly detection problems in Big Data sets, such as credit card fraud.