ASYMPTOTIC EXPANSIONS FOR THE ERGODIC MOMENTS OF A SEMI-MARKOVIAN RANDOM WALK WITH A GENERALIZED DELAYING BARRIER
Year 2012,
Volume 2,
Issue 2,
228 - 237,
01.12.2012
Tahir KHANİYEV
Ali Akbar Fattahpour MARANDİ
Ihsan UNVER
Abstract
In this study, a semi-Markovian random walk process X t with a generalized delaying barrier is considered and the ergodic theorem for this process is proved under some weak conditions. Then, the exact expressions and asymptotic expansions for the first four ergodic moments of the process X t are obtained
References
- Aliyev, R. T., Khaniyev, T. A. and Kesemen, T., (2010), Asymptotic expansions for the moments of a semi-Markovian random walk with gamma distributed interference of chance, Communications in Statistics-Theory and Methods, 39, 130-143.
- Aliyev, R., Kucuk, Z. and Khaniyev, T., (2010), Three-term asymptotic expansions for the moments of the random walk with triangular distributed interference of chance, Applied Mathematical Modeling, 34(11), 3599-3607.
- Aras, G. and Woodroofe, M., (1993), Asymptotic expansions for the moments of a randomly stopped average, Annals of Statistics, 21, 503-519.
- Borovkov, A. A., (1984), Asymptotic Methods in Queuing Theory, John Wiley, New York.
- Chang, J. T. and Peres, Y., (1997), Ladder heights, Gaussian random walks and Riemann zeta function, Annals of Probability, 25, 782-802.
- Chang, J. T., (1992), On moments of the first ladder height of random walks with small drift, Annals of Applied Probability, 2, 714-738.
- El-Shehawey, M. A., (1992), Limit distribution of first hitting time of delayed random walk, Journal of Indian Society of Operation Research, 13(1-4), 63-72.
- Feller, W., (1971), An Introduction to Probability Theory and Its Applications II, John Wiley, New York.
- Gihman, I. I. and Skorohod, A. V., (1975), Theory of Stochastic Processes II, Springer, New York.
- Janssen, A. J. E. M. and Leeuwaarden, J. S. H., (2007), On Lerch’s transcendent and the Gaussian random walk. Annals of Applied Probability, 17(2), 421-439.
- Khaniyev, T. A. and Mammadova, Z. I., (2006), On the stationary characteristics of the extended model of type (s, S) with Gaussian distribution of summands, Journal of Statistical Computation and Simulation, 76(10), 861-874.
- Lotov, V. I., (1996), On some boundary crossing problems for Gaussian random walks, Annals of Probability, 24(4), 2154-2171.
- Rogozin, B. A., (1964), On the distribution of the first jump, Theory of Probability and its Applica- tions, 9(3), 450-464.
Year 2012,
Volume 2,
Issue 2,
228 - 237,
01.12.2012
Tahir KHANİYEV
Ali Akbar Fattahpour MARANDİ
Ihsan UNVER
References
- Aliyev, R. T., Khaniyev, T. A. and Kesemen, T., (2010), Asymptotic expansions for the moments of a semi-Markovian random walk with gamma distributed interference of chance, Communications in Statistics-Theory and Methods, 39, 130-143.
- Aliyev, R., Kucuk, Z. and Khaniyev, T., (2010), Three-term asymptotic expansions for the moments of the random walk with triangular distributed interference of chance, Applied Mathematical Modeling, 34(11), 3599-3607.
- Aras, G. and Woodroofe, M., (1993), Asymptotic expansions for the moments of a randomly stopped average, Annals of Statistics, 21, 503-519.
- Borovkov, A. A., (1984), Asymptotic Methods in Queuing Theory, John Wiley, New York.
- Chang, J. T. and Peres, Y., (1997), Ladder heights, Gaussian random walks and Riemann zeta function, Annals of Probability, 25, 782-802.
- Chang, J. T., (1992), On moments of the first ladder height of random walks with small drift, Annals of Applied Probability, 2, 714-738.
- El-Shehawey, M. A., (1992), Limit distribution of first hitting time of delayed random walk, Journal of Indian Society of Operation Research, 13(1-4), 63-72.
- Feller, W., (1971), An Introduction to Probability Theory and Its Applications II, John Wiley, New York.
- Gihman, I. I. and Skorohod, A. V., (1975), Theory of Stochastic Processes II, Springer, New York.
- Janssen, A. J. E. M. and Leeuwaarden, J. S. H., (2007), On Lerch’s transcendent and the Gaussian random walk. Annals of Applied Probability, 17(2), 421-439.
- Khaniyev, T. A. and Mammadova, Z. I., (2006), On the stationary characteristics of the extended model of type (s, S) with Gaussian distribution of summands, Journal of Statistical Computation and Simulation, 76(10), 861-874.
- Lotov, V. I., (1996), On some boundary crossing problems for Gaussian random walks, Annals of Probability, 24(4), 2154-2171.
- Rogozin, B. A., (1964), On the distribution of the first jump, Theory of Probability and its Applica- tions, 9(3), 450-464.