一类随机环境中单边二重生灭链的常返性  

Recurrence of the Single Side Birth-Death Chain of Order 2 in an Independent Random Environment

作　　者：任敏 REN Min(School of Mathematics and Statistics,Suzhou University,Suzhou,Anhui 234000,China)

机构地区：[1]宿州学院数学与统计学院,安徽宿州234000

出　　处：《河北北方学院学报（自然科学版）》2020年第5期1-4,8,共5页Journal of Hebei North University:Natural Science Edition

基　　金：国家自然科学基金项目(11371029);安徽省质量工程研究项目(2018jyxm0697);宿州学院重点科研项目(2016yzd05);宿州学院重点课程建设研究项目(szxy2018zdkc44)。

摘　　要：目的建立独立不同分布随机环境中的单边二重生灭链模型,研究模型的常返性。方法基于独立同分布随机环境中二重生灭链常返性的判别准则,借助于强大数定理给出模型常返性的判别准则。结果当环境满足一定的条件时,给出独立不同分布随机环境中二重生灭链的常返、正常返、零常返和非常返的判别准则。结论与独立同分布随机环境相比较,独立不同分布随机环境中的单边二重生灭链更接近实际生活。Objective To establish the single side birth-death chain of order 2 in independent non-identically distributed random environment and to discuss the recurrence of the model.Methods Based on the criterion of recurrence of birth-death chain of order 2 in an independent identically distributed random environment,the criterion of recurrence of the model was given by the strong law of large numbers.Results The criterion of recurrence,positive recurrence,null recurrence and transience of single side birth-death chain of order 2 in independent non-identically distributed random environment were given,under the environment that satisfies certain condition.Conclusion Compared with independent identically distributed random environment,the single side birth-death chain of order 2 in an independent non-identically distributed random environment is closer to the real life.

关 键 词：随机环境 单边二重生灭链 常返 非常返 

分 类 号：O211.62[理学—概率论与数理统计]