论文标题
限制分支马尔可夫连锁店的分布
Limit distributions of branching Markov chains
论文作者
论文摘要
我们研究了马尔可夫链在可数的状态空间（类型的空间）上进行分支，$ \ mathscr {x} $，重点关注不断发展的经验人群分布的极限行为的定性方面。除了具有相同的平均水平并满足均匀的$ l \ log l $时刻条件以外，在$ \ mathscr {x} $的点上，在Muthscr {x} $的点上没有任何条件。我们表明，出现的人口马丁格是统一的整合。然后将分支链的总体平均值收敛与$ \ Mathscr {x} $上的相关普通马尔可夫链的固定空间相关（假定是不可约和瞬态的）。特别是将其应用于$ \ Mathscr {x} $的适当压实的边界。最终考虑考虑分支链的理论界限与相关的普通链之间的一般相互作用。
We study branching Markov chains on a countable state space (space of types) $\mathscr{X}$, with the focus on the qualitative aspects of the limit behaviour of the evolving empirical population distributions. No conditions are imposed on the multitype offspring distributions at the points of $\mathscr{X}$ other than to have the same average and to satisfy a uniform $L \log L$ moment condition. We show that the arising population martingale is uniformly integrable. Convergence of population averages of the branching chain is then put in connection with stationary spaces of the associated ordinary Markov chain on $\mathscr{X}$ (assumed to be irreducible and transient). This is applied, in particular, to the boundaries of appropriate compactifications of $\mathscr{X}$. Final considerations consider the general interplay between the measure theoretic boundaries of the branching chain and the associated ordinary chain.
