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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Extends Tweedie's formulae to GBM, BESQ, and CIR processes to enable non-Gaussian diffusion generative models and empirical Bayes applications.
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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.
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Tweedie's Formulae and Diffusion Generative Models Beyond Gaussian
Extends Tweedie's formulae to GBM, BESQ, and CIR processes to enable non-Gaussian diffusion generative models and empirical Bayes applications.