Abstract
A pathwise large deviation result is proved for the pure jump models of the k-nary interacting particle system introduced by Kolokoltsov (Markov Process. Related Fields 12 (2006) 95–138; Nonlinear Markov Processes and Kinetic Equations (2010) Cambridge Univ. Press) that generalize classical Boltzmann’s collision model, Smoluchovski’s coagulation model and many others. The upper bound is obtained by following the standard methods (KOV (Comm. Pure Appl. Math. 42 (1989) 115–137)) of using a process “perturbed” by a regular function. To show the lower bound, we propose a family of orthogonal martingale measures and prove a coupling for the general perturbations. The rate function is studied based on the idea of Léonard (Probab. Theory Related Fields 101 (1995) 1–44) with a simplification by considering the conjugation of integral functionals on a subspace of . General “gelling” solutions in the domain of the rate function are also discussed.
Funding Statement
The author was supported by the National Key R&D Program of China under Grant 2022YFA 1006500. This work was partially conducted while she was a BMS Dirichlet Postdoc in the School of Mathematics, TU Berlin, Germany during Nov 2018–Oct 2021.
Acknowledgments
The author would like to thank the anonymous referees, the Associate Editor and the Editor for their constructive comments that improved the quality of this paper.
Citation
Wen Sun. "Pathwise large deviations for the pure jump k-nary interacting particle systems." Ann. Appl. Probab. 34 (1A) 743 - 794, February 2024. https://doi.org/10.1214/23-AAP1977
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