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 ligh...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.展开更多
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）.
文摘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.
