Spatial birth and death processes
Spatial birth and death processes
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DOI：
10.1017/s0001867800040726
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发表时间：
1975-09
影响因子：
1.2
通讯作者：
C. Preston
中科院分区：
文献类型：
--
作者：
C. Preston
我们研究出生和死亡过程，其中出生/死亡率取决于人口的特定配置。最简单的情况是，当配置构成某些有限晶格的子集时（因此状态空间是有限的）。在这种情况下，我们看看时间可逆性之间的关系，最近邻相互作用，平衡状态是一个马尔可夫随机场。一个更有趣的例子是，可以出生或死亡的实体可以在某个有界空间（或平面）的任何点上出生或死亡。这给了我们一个纯粹的跳跃过程，其一般性质是众所周知的，（例如，参见Feller (1966) Vol. II Chapter X.3）。我们研究了一些特殊的例子并计算了平衡分布。
We examine birth and death processes where the birth/death rates depend on the particular configuration of the population. The easiest case is when the configurations form the subsets of some finite lattice (thus the state space is finite). In this case we look at the relationships between time-reversibility, nearest neighbour interactions, and the equilibrium state being a Markov random field. A more interesting case is when the entities which can be born or die can do so at any point in some bounded region of space (or the plane). This gives us a pure jump process, whose general properties are well-known, (see for example, Feller (1966) Vol. II Chapter X.3). We examine some particular examples and compute equilibrium distributions.