Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2022

Riemann surfaces for integer counting processes

Résumé

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.

Dates et versions

hal-03699851 , version 1 (20-06-2022)

Identifiants

Citer

Sylvain Prolhac. Riemann surfaces for integer counting processes. Journal of Statistical Mechanics: Theory and Experiment, 2022, 2211, pp.113201. ⟨10.1088/1742-5468/ac9615⟩. ⟨hal-03699851⟩
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