Positive Markov processes in Laplace dualityFoucart, Clément (Avtor) Vidmar, Matija (Avtor) positive Markov processduality of semigroupsduality of generatorsLaplace transformcomplete monotonicityLaplace symbolLévy-Khintchine functionmartingale problembranching processstochastic population modelThis article develops a general framework for Laplace duality between positive Markov processes in which the one-dimensional Laplace transform of one process can be represented through that of another. We show that a process admits a Laplace dual if and only if it satisfies a certain complete monotonicity condition. Moreover, we analyse how the conventions adopted for the values of $0 \cdot \infty$ and $\infty \cdot 0$ are reflected in the weak continuity/absorptivity properties of the processes in duality at the boundaries $0$ and $\infty$. A broad class of generators admitting Laplace duals is identified, and we provide sufficient conditions under which the associated martingale problems are well-posed with the solutions being in duality at the level of their semigroups. Laplace duality is shown to furnish a unifying structure for several generalizations of continuous-state branching processes, e.g. those with immigration or evolving in random environments. Along the way, a theorem originally due to Ethier and Kurtz – connecting duality of generators to that of the associated semigroups – is refined, and we provide a concise proof of the Courrège form for the pointwise infinitesimal generator of a positive Markov process whose domain includes the exponential functions. The latter leads naturally to the notion of a Laplace symbol, which is a parsimonious encoding of the infinitesimal dynamics of the process.20262026-08-17 14:54:43Neznano31908UDK: 519.2ISSN pri članku: 1083-6489DOI: 10.1214/26-EJP1582COBISS_ID: 287982851sl