论文标题
整数计数过程的Riemann表面
Riemann surfaces for integer counting processes
论文作者
论文摘要
整数计数过程在基础马尔可夫流程的状态之间的过渡时增加了整数值。计数过程的生成器取决于参数共轭的增量，它通过其特征方程来定义复杂的代数曲线，从而定义了一个紧凑的Riemann表面。我们表明，然后可以将计数过程的概率写成该riemann表面上的轮廓积分。详细讨论了几个示例。
Integer counting processes increment of an integer value at transitions between states of an underlying Markov process. The generator of a counting process, which depends on a parameter conjugate to the increments, defines a complex algebraic curve through its characteristic equation, and thus a compact Riemann surface. We show that the probability of a counting process can then be written as a contour integral on that Riemann surface. Several examples are discussed in details.
