论文标题
时间折段的出生和死亡过程
Time-fractional Birth and Death Processes
论文作者
论文摘要
在本文中，我们为时间分数的出生和死亡过程$n_α（t）$提供了不同的表示，其过渡概率受微分方程的时间分数系统的控制。更具体地说，我们为其轨迹提供了两个等效的特征：第一个作为时间变化的经典出生和死亡过程，而第二个是马尔可夫更新过程。另外，我们为未杀死的过程的渐近行为提供了结果。最重要的是，准限制分布和准平台分布的概念并不重合，这是该过程的长期记忆性质的结果。作为应用程序示例，我们重新审视线性案例以显示我们的主要定理的后果。
In this article, we provide different representations for a time-fractional birth and death process $N_α(t)$, whose transition probabilities are governed by a time-fractional system of differential equations. More specifically, we present two equivalent characterizations for its trajectories: the first one as a time-changed classic birth and death process, whereas the second one is a Markov renewal process. Also, we provide results for the asymptotic behavior of the process conditioned not to be killed. The most important is that the concept of quasi-limiting distribution and quasi-stationary distribution do not coincide, which is a consequence of the long-memory nature of the process. As an application example, we revisit the linear case to show the consequences of our main theorems.
