Light-tailed behavior of stationary distribution for state-dependent random walks on a strip  

作　　者：Wenming HONG Meijuan ZHANG Yiqiang Q. ZHAO 

机构地区：[1]School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, China [2]School of Statistics and Mathematics, Central University of Finance and Economics,Beijing 100081, China [3]School of Mathematics and Statistics, Carleton University, Ottawa, Ont K1S 5B6, Canada

出　　处：《Frontiers of Mathematics in China》2014年第4期813-834,共22页中国高等学校学术文摘·数学（英文）

基　　金：Acknowledgements The authors would like to thank Drs. Hongyan Sun and Ke Zhou for their stimulating discussion. Also they would like to express their gratitude to the referees for their careful reading of the first version of paper and useful suggestions for revising the paper. This work was partially supported by the National Natural Science Foundation of China （Grant No. 11131003）, the 985 Project, and the Natural Sciences and Engineering Research Council of Canada （Grant No. 315660）.

摘　　要：We consider the state-dependent reflecting random walk on a half- strip. We provide explicit criteria for （positive） recurrence, and an explicit expression for the stationary distribution. As a consequence, the light-tailed behavior of the stationary distribution is proved under appropriate conditions. The key idea of the method employed here is the decomposition of the trajectory of the random walk and the main tool is the intrinsic branching structure buried in the random walk on a strip, which is different from the matrix-analytic method.We consider the state-dependent reflecting random walk on a half- strip. We provide explicit criteria for （positive） recurrence, and an explicit expression for the stationary distribution. As a consequence, the light-tailed behavior of the stationary distribution is proved under appropriate conditions. The key idea of the method employed here is the decomposition of the trajectory of the random walk and the main tool is the intrinsic branching structure buried in the random walk on a strip, which is different from the matrix-analytic method.

关 键 词：Random walk on a strip stationary distribution light-tailedbehavior branching process RECURRENCE state-dependent 

分 类 号：O211.62[理学—概率论与数理统计] S811.8[理学—数学]