Abstract
Three different kinds of fluctuation limits (high density fluctuation, small branching fluctuation and large scale fluctuation) of the measure-valued immigration diffusion process are studied, which lead to the generalized Ornstein-Uhlenbeck diffusion defined by a langevin equation of the type of [1]. The fluctuation limit theorems cover all dimension numbers and give physical interpretations to the parameters appearing in the equation.
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This work is supported by the National Natural Science Foundation of China and the Morningside Mathematical Center of the Chinese Academy of Sciences.
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Zenghu, L. Measure-valued immigration diffusions and generalized ornstein-uhlenbeck diffusions. Acta Mathematicae Applicatae Sinica 15, 310–320 (1999). https://doi.org/10.1007/BF02669836
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DOI: https://doi.org/10.1007/BF02669836