发表机构
Southern University of Science & Technology; North Minzu University; Concordia University（南方科技大学; 北方民族大学; 康考迪亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究二维广义连续状态分支过程，其交互由布朗运动和谱正α-稳定随机测度驱动，推导了爆炸/不爆炸及保持无穷/从无穷下降等无穷行为的精确条件。
AI 中文摘要
本文研究了一个二维广义连续状态分支过程，该过程具有相互增强的双向交互作用，由布朗运动和谱正$\alpha$-稳定随机测度驱动的两个随机微分方程刻画。此类连续状态种群动力学也可视为随机Lotka-Volterra型种群模型。在模型所涉及系数的各种条件下，推导了该种群的爆炸/不爆炸以及保持无穷/从无穷下降等无穷行为，所得结论相当精确。
英文摘要
In this paper we consider a two-dimensional generalized continuous-state branching process with mutually enhancing two-way interactions characterized by two stochastic differential equations driven by Brownian motions and spectrally positive $α$-stable random measures. Such continuous-state population dynamics can also be identified as a stochastic Lotka-Volterra type population model. Infinite behavior such as explosion/nonexplosion for this population and staying infinite/coming down from infinity are derived under various conditions on the coefficients involved in the model and the conclusions are rather sharp
