Extinction behaviour for mutually enhancing continuous-state population dynamics

In this paper, we study a two-dimensional process arising as the unique nonnegative solution to a system of two stochastic differential equations (SDEs) with mutually enhancing two-way interactions driven by independent Brownian motions and spectrally positive $\alpha$-stable random measures. Such a SDE system can be identified as a continuous-state Lotka-Volterra type population model. Extinction properties of the populations are studied for different choices of the coefficients involved in the SDEs.