Hydrodynamics of a class of N-urn linear systems

Xiaofeng Xue

Stochastic Processes and their Applications, 2023, vol. 156, issue C, 69-100

Abstract: In this paper we are concerned with hydrodynamics of a class of N-urn linear systems, which include voter models, pair-symmetric exclusion processes and binary contact path processes on N urns as special cases. We show that the hydrodynamic limit of our process is driven by a C[0,1)′-valued linear ordinary differential equation and the fluctuation of our process, i.e, central limit theorem from the hydrodynamic limit, is driven by a C[0,1)′-valued Ornstein–Uhlenbeck process. To derive above main results, we need several replacement lemmas. An extension in linear systems of Chapman–Kolmogorov equation plays key role in proofs of these replacement lemmas.

Keywords: N-urn linear system; Hydrodynamic limit; Non-equilibrium fluctuation (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:156:y:2023:i:c:p:69-100

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DOI: 10.1016/j.spa.2022.11.007

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