广义零程粒子系统生成元的局部有界性

研究了广义零程粒子系统生成元的局部有界性和系统生成元预解算子的局部散逸性.作为粒子系统理论的主要研究对象之一的零程无穷粒子系统,描述了这样一种随机模型,在可列个位置上有无穷个不可辨粒子做随机的移动,同一时刻任何位置上最多只能发生1个粒子转移,粒子转移的概率转移速率仅受该位置的粒子数影响.将上述模型作了推广,研究了在同一时刻任一位置上可以发生任意有限个粒子转移的情形.使用泛函分析的方法,给出了系统的生成元的局部有界性和预解算子的局部散逸性.主要结果为广义零程粒子系统的生成元具有局部有界性,其预解算子具有局部散逸性.

Resolvent operator of generator of generalized infinite particle system with zero range interactions

This paper studies the locally bounded property of a generalized infinite particle system with zero range interactions and the dissipation of the resolvent operator of the system generator.The infinite particle system with zero range interactions,as a major research object in particle system theory,describes such a stochastic model in which there appear to be infinite particles moving at random at a countable number of sites.At any point in time there is only one particle,which is moving from one site to another.We extend this theory to study a situation where there are a finite number of particles moving from one site to another.The probabilistic transition rate depends on the number of particles at a site.The locally bounded property of generator and the local dissipation of the resolvent operator are given by use of the functional method.This paper concludes that the resolvent operator of the generator is locally dissipative and the generator of the system is locally bounded.