Modeling and Estimation of Interactions of Yule-Simon Processes

Yule-Simon processes are preferential attachment processes that can be represented as urn processes where balls are added to a growing number of urns and where a new ball is placed in an urn with probability that is proportional to the number of balls in the urn. In this paper, we consider Yule-Simon processes that interact with each other. We propose two models of interaction, a deterministic and a probabilistic model. Based on observed two processes, we want to determine if the two processes interact and the direction of the interaction. In the case of the probabilistic model, the objective is also to estimate the strength of the interaction. We present detection/estimation schemes for each model. We also provide simulation results that demonstrate the performance of our schemes.