20.500.12556/DiRROS-31908 Positive Markov processes in Laplace duality This 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. positive Markov process duality of semigroups duality of generators Laplace transform complete monotonicity Laplace symbol Lévy-Khintchine function martingale problem branching process stochastic population model pozitiven markovski proces dualnost polgrup dualnost generatorjev Laplaceova transformacija popolna monotonost Laplaceov simbol Lévy-Khintchinova funkcija martingalski problem proces razvejanja stohastični model populacije true false true Angleški jezik Slovenski jezik Neznano 2026-08-17 14:54:43 2026-08-17 14:54:43 2026-08-18 03:47:58 0000-00-00 00:00:00 2026 0 0 str. 1-73 article no. 127 Vol. 31 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-01-01 519.2 1083-6489 10.1214/26-EJP1582 287982851 Download-12.pdf Download-12.pdf 1 E8028C55AFBFB52E49B1C4EFF6CFEB74 fc9da6b940cb7cae6f6208dd6abeb24d3fec62e891ca864219fe8bd21661b124 6d1b929f-9a3b-11f1-af5a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=49636 https://projecteuclid.org/journals/electronic-journal-of-probability/volume-31/issue-none/Positive-Markov-processes-in-Laplace-duality/10.1214/26-EJP1582.full 1 d3881520-9a3a-11f1-af5a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=49635 Inštitut za matematiko, fiziko in mehaniko 0 0 0