论文标题
关于衰减繁殖的人口模型
On decay-surge population models
论文作者
论文摘要
我们考虑连续的时空衰减 - 繁殖种群模型，这些模型是半随机过程，确定性下降的种群被束缚消失，在随机的时间内被随机弥补或随机大小的潮流。在特定的可分离框架（从下面的精确度上）中，我们为规模（或谐波）功能和过程的速度度量提供明确的公式。无穷大的比例功能的行为允许在此过程中制定条件，在这些过程中，该过程爆炸或在Infinity或Harris复发时是短暂的。提供了这种连续时间过程的离散时间嵌入式链和极端记录链的结构的描述。
We consider continuous space-time decay-surge population models which are semi- stochastic processes for which deterministically declining populations, bound to fade away, are rein- vigorated at random times by bursts or surges of random sizes. In a particular separable framework (in a sense made precise below) we provide explicit formulae for the scale (or harmonic) function and the speed measure of the process. The behavior of the scale function at infinity allows to formulate conditions under which such processes either explode or are transient at infinity, or Harris recurrent. A description of the structures of both the discrete-time embedded chain and extreme record chain of such continuous-time processes is supplied.
