February 2024 Pathwise large deviations for the pure jump k-nary interacting particle systems
Wen Sun
Author Affiliations +
Ann. Appl. Probab. 34(1A): 743-794 (February 2024). DOI: 10.1214/23-AAP1977

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 L. 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

Download 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

Information

Received: 1 July 2021; Revised: 1 December 2022; Published: February 2024
First available in Project Euclid: 28 January 2024

MathSciNet: MR4696290
zbMATH: 07829155
Digital Object Identifier: 10.1214/23-AAP1977

Subjects:
Primary: 60F10 , 60G57 , 60J76 , 60K35

Keywords: Becker–Döring coagulation and fragmentation , Boltzmann collision , coupling , large deviation , martingale measure , Measure-valued Markov process , Smoluchowski’s coagulation

Rights: Copyright © 2024 Institute of Mathematical Statistics

Vol.34 • No. 1A • February 2024
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