2012/01/16 by Masahiro Kobayashi, Kobayashi, Masahiro, Masakiyo Miyazawa +1
Economics, Econometrics and Finance · Mathematics · #60J10 #60K25 #68M10 #90B15 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60J10 #msc:60K25 #msc:68M10 #msc:90B15
paper · pdf · doi:10.48550/arxiv.1201.3167
40 pages, 8 figures; Proceedings for MAM 7, 2012
arxiv created 2012/01/16 · openalex publication_date 2012/01/16 · arxiv updated 2012/01/17 · openalex created_date 2019/09/05 · openalex updated_date 2026/07/28
We consider a two dimensional skip-free reflecting random walk on a nonnegative integer quadrant. We are interested in the tail asymptotics of its stationary distribution, provided its existence is assumed. We derive exact tail asymptotics for the stationary probabilities on the coordinate axis. This refines the asymptotic results in the literature, and completely solves the tail asymptotic problem on the stationary marginal distributions in the coordinate and diagonal directions. For this, we use the so-called analytic function method in such a way that either generating functions or moment generating functions are suitably chosen. The results are exemplified by a two node network with simultaneous arrivals.