Poisson Process Driven Stochastic Differential Equations for bivariate heavy tailed distributions

Stochastic differential equations have been used intensively in stochastic control. In this paper, we present 2-dimensional Poisson Counter Driven Stochastic Differential Equation (PCSDE) models that lead to correlated bivariated power law behaviors. We propose two types of 2D PCSDE models and study their tail dependence behavior. The first model generates tail dependence coefficient with values either 0 or 1; while the second model could have the values between 0 and 1. We discuss plausible application of our models in complex network generative models.