In this paper we introduce a novel continuous-time counting stochastic process that we call non-homogeneous compound-birth process. Our motivation is to apply this process in insurance risk theory and queueing theory. To this aim, we study the process in more detail and provide an iterative formula for its transition probabilities. We also deduce the process's probability generating function in a very general particular case, followed by some applications and examples.

中文翻译：

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引入非均匀复合出生过程

在本文中，我们介绍了一种新颖的连续时间计数随机过程，我们称其为非均质复合出生过程。我们的动机是将此过程应用于保险风险理论和排队论。为此，我们将更详细地研究该过程，并为其过渡概率提供一个迭代公式。我们还将在一个非常特殊的情况下推论出过程的概率生成函数，然后介绍一些应用程序和示例。