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.
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.
