| Title: | Positive Markov processes in Laplace duality |
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| Authors: | ID Foucart, Clément (Author)
ID Vidmar, Matija (Author) |
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| Files: |  PDF - Presentation file, download (1,28 MB)
MD5: E8028C55AFBFB52E49B1C4EFF6CFEB74
 URL - Source URL, visit https://projecteuclid.org/journals/electronic-journal-of-probability/volume-31/issue-none/Positive-Markov-processes-in-Laplace-duality/10.1214/26-EJP1582.full
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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. |
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| Keywords: | 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 |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | str. 1-73 |
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| Numbering: | Vol. 31, article no. 127 |
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| PID: | 20.500.12556/DiRROS-31908  |
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| UDC: | 519.2 |
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| ISSN on article: | 1083-6489 |
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| DOI: | 10.1214/26-EJP1582 |
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| COBISS.SI-ID: | 287982851 |
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| Note: |
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| Publication date in DiRROS: | 17.08.2026 |
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| Views: | 42 |
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| Downloads: | 19 |
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