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首页> 外文期刊>The Annals of Probability: An Official Journal of the Institute of Mathematical Statistics >QUASI-STATIONARY DISTRIBUTIONS AND DIFFUSION MODELSIN POPULATION DYNAMICS
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QUASI-STATIONARY DISTRIBUTIONS AND DIFFUSION MODELSIN POPULATION DYNAMICS

机译：人口动力学中的准平稳分布和扩散模型

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摘要

In this paper we study quasi-stationarity for a large class of Kolmogorovdiffusions. The main novelty here is that we allow the drift to go to —oo at theorigin, and the diffusion to have an entrance boundary at -Pcx). These diffu-sions arise as images, by a deterministic map, of generalized Feller diffusions,which themselves are obtained as limits of resealed birth—death processes.Generalized Feller diffusions take nonnegative values and are absorbed atzero in finite time with probability 1. An important example is the logisticFeller diffusion. We give sufficient conditions on the drift near 0 and near +cc for the ex-istence of quasi-stationary distributions, as well as rate of convergence in theYaglom limit and existence of the Q-process. We also show that, under theseconditions, there is exactly one quasi-stationary distribution, and that this dis-tribution attracts all initial distributions under the conditional evolution, ifand only if H-oo is an entrance boundary. In particular, this gives a sufficientcondition for the uniqueness of quasi-stationary distributions. In the proofsspectral theory plays an important role on L2 of the reference measure forthe killed process.
机译：在本文中，我们研究了一大类Kolmogorov扩散的准平稳性。这里的主要新颖之处在于，我们允许漂移在原点处变为-oo，并且扩散的入口边界处为-Pcx。这些扩散通过确定性图的图像出现，作为广义Feller扩散的图像，它们本身是作为重新密封的出生-死亡过程的极限而获得的。广义Feller扩散采用非负值，并在有限的时间内以概率1零吸收。例如logisticFeller扩散。对于准平稳分布的存在，Yaglom极限中的收敛速度和Q过程的存在，我们为0附近和+ cc附近的漂移给出了充分的条件。我们还表明，在这些条件下，仅存在一个准平稳分布，并且仅当H-oo是入口边界时，这种分布才会吸引条件演化下的所有初始分布。特别是，这为准平稳分布的唯一性提供了充分的条件。在证明中，光谱理论对被杀死过程的参考度量的L2起着重要作用。

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