Path-Wise Large Deviations For The Pure Jump K-Nary Interacting Particle Systems
数学专题报告
报告题目(Title)：Path-Wise Large Deviations For The Pure Jump K-Nary Interacting Particle Systems
报告人(Speaker)：孙雯 副教授（中国科学技术大学）
地点(Place)：后主楼1225
时间(Time)：2022年1月6日 下午3.00-4.00
邀请人(Inviter)：何辉
报告摘要
A pathwise large deviation result is proved for the pure jump models of k-nary interacting particle system introduced by Kolokoltsov that generalize classical Boltzmann's collision model, Smoluchovski's coagulation model, Becker-D\"oring's Coagulation and Fragmentation model and many others. The upper bound is obtained by following the standard methods (Kipnis-Olla-Varadhan) 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 L��onard with a simplification by considering the conjugation of integral functionals on a subspace of $L^\infty$. General ``gelling" solutions in the domain of the rate function are also discussed.
