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Original Articles

On the semi-Markovian random walk with two reflecting barriers

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Pages 799-819 | Published online: 15 Feb 2007

REFERENCES

  • Afanas'eva , L.G. and Bulinskaya , E.V. 1984 . Some asymptotic results for random walks in a strip . Theory Probability and its Applications , 29 ( 4 ) : 654 – 668 .
  • Borovkov , A.A. 1972 . Stochastic Proc. in the Theory of Queues Moscow : Nauka . 368pp.
  • Borovkov , A.A. 1980 . Asymptotical Methods in The Theory Of Queues Moscow : Nauka . 384pp.
  • Borovkov , A.A. 1975 . On the random walk in the strip with two delaying barriers . Math. Zametki , 17 ( 4 ) : 647 – 657 .
  • El-Shehawey , M.A. 1992 . Limit distribution of first hitting time of delayed random walk . J. Indian Soc. Oper. Res. , 13 ( 1–4 ) : 63 – 72 .
  • Feller , W. 1971 . An Introduction To Probability Theory And Its Applications II New York : John Wiley & Sons, Inc. . 670pp.
  • Kastenbaum , M.A. 1966 . A dialysis system with one absorbing and one semireflecting state . J. Appl. Probab. , 3 : 363 – 371 .
  • Khaniev , T.A. 1984 . “ Distribution of a semi-Markovian random walk with two delaying screens ” . In Some Question Of The Theory Of Stochastic Processes Edited by: Skorohod , A.V. 106 – 113 . Kiev : Naukova Dumka .
  • Khaniev , T.A. and özdemir , H. 1995 . “ On the Laplace transform of finite-dimensional distribution functions of semi-continuous random processes with reflecting and delaying screens ” . In Exploring Stochastic Laws Edited by: Skorohod , A.V. and Borovskikh , Yu.V. 167 – 174 . Zeist, The Netherlands : VPS .
  • Khaniev , T.A. and Unver , I. 1997 . The Study of the Level Zero Crossing Time of Semi-Markovian Random Walk with Delaying Screen . Turkish Journal of Mathematics , 21 ( 3 ) : 257 – 268 .
  • Khaniev , T.A. , Ozdemir , H. and Maden , S. 1998 . Calculating the Probability Characteristics of a Boundary Functional of a Semi-Continuous Random Process with Reflecting and Delaying Screens . Applied Stochastic Models and Data Analysis , 14 ( 3 ) : 117 – 123 .
  • Khaniev , T.A. 2000 . Some Asymptotic Results for Ergodic Distribution of the Semi-Markovian Random Walk with Special Barrier . Journal of Institute of Mathematics and Computer Sciences (Mathematics Series) , 13 ( 2 ) : 203 – 209 .
  • Korolyuk , V.S. and Borovskikh , Yu.V. 1981 . Analytical Problems for Asymptotics of Probability Distributions Kiev : Naukova Dumka . 240pp.
  • Lotov , V.I. 1991 . On random walks within a stripe . Theory Probability and Its Applications , 36 ( 1 ) : 160 – 165 .
  • Lotov , V.I. 1991 . On the asymptotics of distributions in two-sided boundary problems for random walks defined on a Markov chain . Sib. Adv. Math. , 1 ( 3 ) : 26 – 51 .
  • Nasirova , T.I. 1984 . Proc. Of The Semi-Markovian Random Walks Baku : ELM . 169pp.
  • Prabhu , N.U. 1981 . Stochastic Storage Processes New York : Springer-Verlag . 140pp.
  • Skorohod , A.V. and Slobedenyuk , N.P. 1970 . Limit Theorems For The Random Walks Kiev : Naukova Dumka . 302pp.
  • Spitzer , F. 1964 . Principles of Random Walk Princeton : Van Nostrand . 406pp.
  • Takacs , L. 1977 . Combinatorical Methods In The Theory Of Stochastic Processes New York : Robert E. Krieger Publishing Company XI . 264pp.
  • Unver , I. 1997 . On Distributions of the Semi-Markovian Random Walk with Reflecting and Delaying Barriers . Bull. Cal. Math. Soc. , 89 ( 4 ) : 231 – 242 .
  • Weesakul , B. 1961 . The random walk between a reflecting and an absorbing barrier . Ann. Math. Statis. , 32 : 765 – 773 .
  • Zhang , Y.L. 1992 . Some problems on a one dimensional correlated random walk with various types of barrier . J. Appl. Probab. , 29 : 196 – 201 .

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