Exact asymptotic formulae of the stationary distribution of a discrete-time two-dimensional QBD process
Exact asymptotic formulae of the stationary distribution of a discrete-time two-dimensional QBD process
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DOI：
10.1007/s11134-018-9586-x
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发表时间：
2017-07
期刊：
影响因子：
1.2
通讯作者：
Toshihisa Ozawa;Masahiro Kobayashi
中科院分区：
文献类型：
--
作者：
Toshihisa Ozawa;Masahiro Kobayashi
本文考虑有限集上带有补充过程的离散二维过程，其中单个过程和都是无跳的。我们假设联合过程Y_n =（X_{1，n}，X_{2，n}，J_n）是马尔可夫过程，并且二维过程的转移概率依赖于补充过程的状态而被调制。这种调制是空间均匀的，除了的边界。我们称这个过程为离散时间二维拟生灭过程。在一定条件下，得到了平稳分布在坐标方向上的精确渐近公式。
We consider a discrete-time two-dimensional processonwith a supplemental processon a finite set, where the individual processesandare both skip-free. We assume that the joint process $$\{\varvec{Y}_n\}=\{(X_{1,n},X_{2,n},J_n)\}$$ is Markovian and that the transition probabilities of the two-dimensional processare modulated depending on the state of the supplemental process. This modulation is space homogeneous except for the boundaries of. We call this process a discrete-time two-dimensional quasi-birth-and-death process. Under several conditions, we obtain the exact asymptotic formulae of the stationary distribution in the coordinate directions.