Local Asymptotics of a Markov Modulated Random Walk with Heavy-tailed Increments  

作　　者：Bing Chang WANG Yuan Yuan LIU 

机构地区：[1]Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China [2]School of Mathematics, Railway Campus, Central South University, Changsha 410075, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第9期1843-1854,共12页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China （Grant Nos. 10901164 and 10771216） and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education We are grateful to Professor Zhenting Hou and the referees for many valuable comments on the draft of this paper. In particular, we wish to thank a referee for pointing out a related new topic stated in Remark 3.9.

摘　　要：In this paper, we obtain sufficient and necessary conditions for local asymptotics for the maximum of a Markov modulated random walk with long-tailed increments and negative drifts, where the local asymptotics means asymptotic behaviour of P（ ∈ （x,x ＋ z]） for each z 〉 0, as x→∞ Our results extend and improve the existing ones in the literature.In this paper, we obtain sufficient and necessary conditions for local asymptotics for the maximum of a Markov modulated random walk with long-tailed increments and negative drifts, where the local asymptotics means asymptotic behaviour of P（ ∈ （x,x ＋ z]） for each z 〉 0, as x→∞ Our results extend and improve the existing ones in the literature.

关 键 词：Mavkov modulated random walk local asymptotics long-tailed distributions subexpo- nential distributions Wiener-Hopf factorization 

分 类 号：TN919.81[电子电信—通信与信息系统] V241.558[电子电信—信息与通信工程]