Frontiers of Mathematics in China >
Light-tailed behavior of stationary distribution for state-dependent random walks on a strip
Received date: 15 Apr 2014
Accepted date: 07 May 2014
Published date: 20 Aug 2014
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We consider the state-dependent reflecting random walk on a halfstrip. 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.
Wenming HONG , Meijuan ZHANG , Yiqiang Q. ZHAO . Light-tailed behavior of stationary distribution for state-dependent random walks on a strip[J]. Frontiers of Mathematics in China, 2014 , 9(4) : 813 -834 . DOI: 10.1007/s11464-014-0405-3
| 1 |
Bolthausen E, Goldsheid I. Recurrence and transience of random walks in random environments on a strip. Comm Math Phys, 2000, 214: 429-447
|
| 2 |
Bright L W, Taylor P G. Equilibrium distributions for level-dependent 1uasi-birth-anddeath processes. In: Chakravarthy S R, Alfa A S, eds. Matrix Analytic Methods in Stochastic Models: Proc of the 1st Int Conf. New York: Marcel Dekker, 1997, 359-375
|
| 3 |
Durrett R. Probability: Theory and Examples. 3rd ed. Belmont: Duxbury, 2004
|
| 4 |
Dwass M. Branching processes in simple random walk. Proc Amer Math Soc, 1975, 51: 270-274
|
| 5 |
Falin G I, Templeton J G C. Retrial Queues. London: Chapman & Hall, 1997
|
| 6 |
Hong W M, Wang H M. Intrinsic branching structure within (L- 1) random walk in random environment and its applications. Infin Dimens Anal Quantum Probab Relat Top, 2013, 16(1): 1350006 (14 pp)
|
| 7 |
Hong W M, Zhang L. Branching structure for the transient (1,R)-random walk in random environment and its applications. Infin Dimens Anal Quantum Probab Relat Top, 2010, 13: 589-618
|
| 8 |
Hong W M, Zhang M J. Branching structure for the transient random walk in a random environment on a strip and its application. Preprint, 2012
|
| 9 |
Horn R A, Johnson C R. Matrix Analysis. Cambridge: Cambridge University Press, 1990
|
| 10 |
Kesten H, Kozlov M V, Spitzer F. A limit law for random walk in a random environment. Compos Math, 1975, 30: 145-168
|
| 11 |
Krause G M. Bounds for the variation of matrix eigenvalues and polynomial roots. Linear Algebra Appl, 1994, 208: 73-82
|
| 12 |
Latouche G, Ramaswami V. Introduction to Matrix Analytic Methods in Stochastic Modeling. Philadelphia: SIAM, 1999
|
| 13 |
Miyazawa M, Zhao Y Q. The stationary tail asymptotics in the GI/G/1 type queue with countably many background states. Adv Appl Probab, 2004, 36(4): 1231-1251
|
| 14 |
Ostrowski A. Solution of Equations in Euclidean and Banach Space. New York: Academic Press, Inc, 1973
|
| 15 |
Zhao Y Q. Censoring technique in studying block-structured Markov chains. In: Latouche G, Taylor P, eds. Advances in Algorithmic Methods for Stochastic Models. NJ: Notable Publications, Inc, 2000, 417-433
|
| 16 |
Zhao Y Q, Li W, Braun W J. Censoring, factorizations, and spectral analysis for transition matrices with block-repeating entries. Methodol Comput Appl Probab, 2003, 5: 35-58
|
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