超指数种群增长模型的确定性与随机性
Deterministic versus stochastic aspects of superexponential population growth models
摘要：
具有幂律速率的确定性种群增长模型可以表现出从代数、指数到超指数（有限时间爆炸）的各种增长行为。在这种设置中，自相似性的考虑发挥了关键作用，连同两个时间替换。两个随机版本的这样的模型进行了研究，表现出更丰富的各种行为。一种是基于谱正过程的指数化的自相似正随机过程的Lamperti构造，随后是适当的时间变化。另一个是基于稳定的连续状态分支过程，给出了另一个Lamperti时间替换适用于稳定的谱正过程。
英文摘要：
Deterministic population growth models with power-law rates can exhibit a large variety of growth behaviors, ranging from algebraic, exponential to hyperexponential (finite time explosion). In this setup, selfsimilarity considerations play a key role, together with two time substitutions. Two stochastic versions of such models are investigated, showing a much richer variety of behaviors. One is the Lamperti construction of selfsimilar positive stochastic processes based on the exponentiation of spectrally positive processes , followed by an appropriate time change. The other one is based on stable continuous-state branching processes, given by another Lamperti time substitution applied to stable spectrally positive processes.
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