论文标题
线性竞争过程和带有拆卸的广义polya urns
Linear competition processes and generalized Polya urns with removals
论文作者
论文摘要
竞争过程是一个连续的时间马尔可夫链，可以解释为一种相互作用的出生和死亡过程的系统，其成分的成分可以通过竞争性相互作用而发展。本文致力于研究这种竞争过程的长期行为，在该过程中，该过程的组成部分随线性出生率而增加，并随着其他组件的线性函数给出的速率降低。零是每个组件的吸收状态，也就是说，当组件变为零时，它永远保持零（我们说此组件已灭绝）。我们表明，概率是，最终只有该过程的非相互作用组成部分的一个随机子集幸存下来。相关的带有拆卸的广义Polya urn模型也有类似的结果。
A competition process is a continuous time Markov chain that can be interpreted as a system of interacting birth-and-death processes, the components of which evolve subject to a competitive interaction. This paper is devoted to the study of the long-term behaviour of such a competition process, where a component of the process increases with a linear birth rate and decreases with a rate given by a linear function of other components. A zero is an absorbing state for each component, that is, when a component becomes zero, it stays zero forever (and we say that this component becomes extinct). We show that, with probability one, eventually only a random subset of non-interacting components of the process survives. A similar result also holds for the relevant generalized Polya urn model with removals.
