Bridges of Markov counting processes. Reciprocal classes and duality formulas

TL;DR

This paper investigates reciprocal classes of Markov counting processes, identifying their invariants and characterizing them through duality formulas, thus advancing understanding of their structural properties.

Contribution

It introduces a novel characterization of reciprocal classes of Markov counting processes using reciprocal invariants and duality formulas.

Findings

Identification of reciprocal invariants for Markov counting processes

Characterization of reciprocal classes via duality formulas

Enhanced understanding of the structure of counting process bridges

Abstract

Processes having the same bridges are said to belong to the same reciprocal class. In this article we analyze reciprocal classes of Markov counting processes by identifying their reciprocal invariants and we characterize them as the set of counting processes satisfying some duality formula.