The paper establishes Laplace duality for continuous-state branching processes with Lévy-Khintchine drift-interaction and constructs Fellerian extensions with parameters determining boundary behaviors at 0 and infinity.
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The paper introduces Laplace duality for positive Markov processes, proves it holds iff a complete monotonicity condition is met, identifies a broad class of generators, and refines the Ethier-Kurtz theorem linking generator duality to semigroup duality.
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Continuous-state branching processes with L\'evy-Khintchine drift-interaction: Laplace duality and Fellerian extensions
The paper establishes Laplace duality for continuous-state branching processes with Lévy-Khintchine drift-interaction and constructs Fellerian extensions with parameters determining boundary behaviors at 0 and infinity.
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Positive Markov processes in Laplace duality
The paper introduces Laplace duality for positive Markov processes, proves it holds iff a complete monotonicity condition is met, identifies a broad class of generators, and refines the Ethier-Kurtz theorem linking generator duality to semigroup duality.