Tutan Bariyerli Yarı-Markov Rastgele Yürüyüş Sıçrama Sürecinin Alt Sınır Fonksiyonelinin Dağılımı

Bu çalışmada sıfır seviyesinde tutan bariyerli bir yarı-Markov rastgele yürüyüş basamak süreci kurulmuş ve bu sürecin tutan bariyere ilk kez düşme anının dağılımının Laplace dönüşümüm elde edilmiştir. Ayrıca sürecin bir sınır fonksiyonalinin beklenen değer ve standart sapması verilmiştir

Anahtar Kelimeler:

Tutan bariyer, Laplace dönüşümü, Yarı-markov rastgele yürüyüş

Distribution of the Lower Boundary Functional of the Step Process of Semi-Markov Random Walk with Delaying Barrier

In this paper, a step process of semi-Markovian random walk with delaying barrier on the zero-level is constructed and the Laplace transformation of the distribution of first crossing time of this process into the delaying barrier is obtained. Also, the expectation and standard diversion of a boundary functional of the process are given.

Keywords:

Semi-Markovian Random Walk, Delaying Screen, Laplace Transformation.,

PDF

___

1. Afanas’eva, LG., Bulinskaya, EV. 1983. Some Asymptotical Results for Random Walks in A Strip. Teor. Veroyatn. Primen., 29 (4): 658-668.
2. Borovkov, AA. 1972. Stochastic Processes in The Theory of Queues. Nauka, Moscow.
3. Feller, W. 1968. An Introduction to Probability Theory and Its Applications. Vol. I, Wiley, New York.
4. Gihman, II., Skorohod, AV. 1975. The Theory of Stochastic Processes II. Springer-Verlag.
5. Khaniev, TA., Ünver, I. 1997. The Study of The Level Zero Crossing Time of A Semi-Markov Random Walk with Delaying Screen. Tr. J. Math., 21: 257-268.
6. 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.
7. Nasirova, TI. 1984. Processes of Semi-Markov Walk, ELM, Baku.
8. Nasirova, TI., Omarova, KK. 2017. Distribution of The Lower Boundary Functional of The Step Process of SemiMarkov Random Walk with Delaying Barrier at Zero, Ukrainian Math. J., 59 (7): 1010–1018.
9. Nasirova, TI., Sadikova, RI. 2009. Laplace Transformation of the Distribution of the Time of System Sojourns within a Band. Auto. Cont. and Comp. Sci., 43 (4): 190–194.
10. Nasirova, TI., Shamilova, BG. 2014. Investigation of Some Probabilistic Characteristics of One Class of Semi Markov Wandering with Delaying Screens. Auto. Cont. and Comp. Sci., 48 (2): 109–119.
11. Nasirova, TI., Sadikova, RI., Ibaev, EA. 2015. Determination of the Mean and Mean Square Deviations of the System Level. Auto. Cont. and Comp. Sci., 49 (1): 37–45.
12. Omarova, KK., Bakhshiev, SB. 2010. The Laplace Transform for the Distribution of The Lower Bound Functional in a Semi Markov Walk Process with a Delay Screen at Zero’, Auto. Cont. and Comp. Sci. 44 (4): 246-252.
13. Prabhu, NU. 1981. Stochastic Storage Processes. New York, Heidelberg: Springer- Verlag.
14. Spitzer, F. 1969. Principles of Random Walk. Van Nostrand, Princeton.