Gang Rivalry Dynamics via Coupled Point Process

We introduce a point process model for inter-gang violence driven by retaliation – a core feature of gang behavior – and multi-party inhibition. Here, a coupled system of statedependent jump stochastic differential equations is used to model the conditional intensities of the directed network of gang rivalries. The system admits an exact simulation strategy based upon Poisson thinning. The model produces a wide variety of transient or stationary weighted network configurations and we investigate under what conditions each type of network forms in the continuum limit. We then fit the model to gang violence data provided by the Hollenbeck district of the Los Angeles Police Department to measure the levels of excitation and inhibition present in gang violence dynamics, as well as the stability of gang rivalries in Hollenbeck.