关于衰减-激增种群模型
On decay-surge population models
摘要：
我们考虑连续时空衰减-激增种群模型，这些模型是半随机过程，其中确定性下降的种群必然会消失，但在随机时间会通过随机大小的爆发或激增而重新焕发活力。在一个特定的可分离框架（在某种意义上说，下面精确），我们提供了明确的公式的规模（或谐波）功能和速度措施的过程。尺度函数在无穷远处的行为允许制定条件，在这些条件下，这些过程要么爆炸，要么在无穷远处是瞬态的，要么是Harris经常性的。给出了这类连续过程的离散时间嵌入链和极值记录链的结构描述。
英文摘要：
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.
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