Riemann surfaces for integer counting processes
arXiv:2206.01698 · doi:10.1088/1742-5468/ac9615
Abstract
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.
arXiv comment52 pages, 15 figures, 6 tables
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