随机逻辑斯谛过程的入侵概率、命中时间和某些涨落理论
Invasion probabilities, hitting times, and some fluctuation theory for the stochastic logistic process
摘要：
我们考虑一类随机过程的游览描述人口的离散个体经历密度有限的增长，使人口具有有限的承载能力和行为定性像经典的Logistic模型时，承载能力是大的。然而，作为离散和随机的，我们的种群仍然会在有限的时间内灭绝。我们目前的结果，最大的人口灭绝前的大人口的限制，从中我们得到建立概率和上界的过程中，以及估计的等待时间建立和灭绝。因此，我们表明，有条件的建立，随机逻辑过程将以高概率大大超过承载能力的任意次数之前灭绝。
英文摘要：
We consider excursions for a class of stochastic processes describing a population of discrete individuals experiencing density-limited growth, such that the population has a finite carrying capacity and behaves qualitatively like the classical logistic model when the carrying capacity is large. Being discrete and stochastic, however, our population nonetheless goes extinct in finite time. We present results concerning the maximum of the population prior to extinction in the large population limit, from which we obtain establishment probabilities and upper bounds for the process, as well as estimates for the waiting time to establishment and extinction. As a consequence, we show that conditional upon establishment, the stochastic logistic process will with high probability greatly exceed carrying capacity an arbitrary number of times prior to extinction.
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