In this paper, we present the testing of four hypotheses on two streams of observations that are driven by Lévy processes. This is applicable for sequential decision making on the state of two-sensor systems. In one case, each sensor receives or does not receive a signal obstructed by noise. In another, each sensor receives data driven by Lévy processes with large or small jumps. In either case, these give rise to four possibilities. Infinitesimal generators are presented and analyzed. Bounds for infinitesimal generators in terms of super-solutions and sub-solutions are computed. An application of this procedure for stochastic model is also presented in relation to the financial market.

中文翻译：

---

用于二维Lévy过程驱动假设检验的无穷小生成器

在本文中，我们介绍了在Lévy过程驱动的两个观测流上对四个假设的检验。这适用于对两个传感器系统的状态进行顺序决策。在一种情况下，每个传感器都接收或不接收被噪声阻塞的信号。在另一个传感器中，每个传感器都接收由Lévy进程驱动的数据，其跳跃大小不一。在任何一种情况下，这些都会产生四种可能性。提出并分析了无穷小生成器。计算了超小子生成器在超解和子解方面的边界。还针对金融市场介绍了此过程在随机模型中的应用。