Definition of Laplace Transforms for Distribution of the First Passage of Zero Level of the Semi-Markov Random Process with Positive Tendency and Negative Jump

ABSTRACT

One of the important problems of stochastic process theory is to define the Laplace transforms for the distribution of semi-markov random processes. With this purpose, we will investigate the semimarkov random processes with positive tendency and negative jump in this article. The first passage of the zero level of the process will be included as a random variable. The Laplace transforms for the distribution of this random variable is defined. The parameters of the distribution will be calculated on the basis of the final results.

One of the important problems of stochastic process theory is to define the Laplace transforms for the distribution of semi-markov random processes. With this purpose, we will investigate the semimarkov random processes with positive tendency and negative jump in this article. The first passage of the zero level of the process will be included as a random variable. The Laplace transforms for the distribution of this random variable is defined. The parameters of the distribution will be calculated on the basis of the final results.

KEYWORDS

Laplace Transforms, Semi-Markov Random Process, Random Variable, Process with Positive Tendency and Negative Jumps

Laplace Transforms, Semi-Markov Random Process, Random Variable, Process with Positive Tendency and Negative Jumps

Cite this paper

nullT. Nasirova and U. Kerimova, "Definition of Laplace Transforms for Distribution of the First Passage of Zero Level of the Semi-Markov Random Process with Positive Tendency and Negative Jump,"*Applied Mathematics*, Vol. 2 No. 7, 2011, pp. 908-911. doi: 10.4236/am.2011.27122.

nullT. Nasirova and U. Kerimova, "Definition of Laplace Transforms for Distribution of the First Passage of Zero Level of the Semi-Markov Random Process with Positive Tendency and Negative Jump,"

References

[1] Borovkov. A. A. 2004. On the Asymptotic Behavior of the Distributions of First- Passage, Mat. Zametki, 2004, Volume 75:1, 24-39

[2] Lotov V. I. On the asymptotics of the distributions in two-sided boundary problems for random walks defined on a Markov chain. Siberian Advances in Math., 1991, V. 1, No. 3, 26-51

[3] Klimov. G. P. 1966. Stochastic queuening systems, Moscow: Nauka.

[4] T. I. Nasirova and R. I. Sadikova Laplace transformation of the distribution of the time of system sojourns within a band. Automatic Control and computer sciences, Volume43, Number4, 190-194

[1] Borovkov. A. A. 2004. On the Asymptotic Behavior of the Distributions of First- Passage, Mat. Zametki, 2004, Volume 75:1, 24-39

[2] Lotov V. I. On the asymptotics of the distributions in two-sided boundary problems for random walks defined on a Markov chain. Siberian Advances in Math., 1991, V. 1, No. 3, 26-51

[3] Klimov. G. P. 1966. Stochastic queuening systems, Moscow: Nauka.

[4] T. I. Nasirova and R. I. Sadikova Laplace transformation of the distribution of the time of system sojourns within a band. Automatic Control and computer sciences, Volume43, Number4, 190-194