Rescaled generalized Derrida-Retaux dynamics converge in Skorokhod space to a continuous-time process whose semigroup, generator, and martingale problem are characterized.
Asymptotic behavior of the generalized Derrida-Retaux recursive model
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abstract
We study the max-type recursive model introduced by Hu and Shi (J. Stat. Phys., 2018), which generalizes the model of Derrida and Retaux (J. Stat. Phys., 2014). The class of geometric-type marginal distributions is preserved by the model with a geometric offspring distribution. We give some long-time asymptotic expansions of the parameters of the marginal distribution. From the expansions, we derive the asymptotics of the sustainability probability, marginal distribution, first moment and probability generating function.
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Derrida-Retaux type models and related scaling limit theorems
Rescaled generalized Derrida-Retaux dynamics converge in Skorokhod space to a continuous-time process whose semigroup, generator, and martingale problem are characterized.