RESEARCH OF THE SEMI-MARKOVIAN PROCESS IN CONDITIONS OF LIMITEDLY RARE CHANGES IN ITS STATE
- Autores: Gorbatenko A.E.1, Nazarov A.A.1
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Afiliações:
- Tomsk State University
- Edição: Volume 11, Nº 7 (2010)
- Páginas: 44-48
- Seção: Articles
- URL: https://journals.eco-vector.com/2712-8970/article/view/505670
- ID: 505670
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Texto integral
Resumo
In this work the SM-flow in conditions of limitedly rare changes in its states is considered. In the proposed asymptotic condition there is a probable distribution of a number of events coming from the SM-flow in time t. We have shown that this distribution can be multimodal.
Texto integral
In this work the SM-process has been considered [1]; it is the general flow of flow models with homogeneous events. We shall give a definition of the Semi-Markovian (SM) process. For this purpose we have considered a twodimensional homogeneous Markovian stochastic process {ξ (n), τ (n)} with a discrete time. Here ξ (n) the ercodic Markov chain with a discrete time and matrix P = [pνk] accept the probabilities of transition for one step [2]; the process τ(n) accepts non-negative values from the continuous set. Then we determine the Markovian transition function F(ν, x, k, y) for the process {ξ(n), τ(n)}: ( ) { ( ) ( ) ( ) ( ) } , ; , 1 , 1 , . F k x y P n k n x n n y ν = ξ - = τ - < ξ =ν τ We shall consider two-dimensional processes such as {ξ (n), τ (n)} for which the following equalities are correct: F (ν, x; k, y) = F (ν, x; k ) , that is F(ν, x, k, y) does not depend on the values of the y process τ(n). Denote ( ) ( ) { ( ) ( ) ( ) } , ; 1 , 1 . k F k x A x P n k n x n ν ν = = ξ - = τ - < ξ =ν (1) Matrix A(x) with elements Aνk (x) can be called SemiMarkovian.×
Sobre autores
A. Gorbatenko
Tomsk State UniversityRussia, Tomsk
A. Nazarov
Tomsk State UniversityRussia, Tomsk
Bibliografia
- Lopukhova S. V. The asymptotic and numerical methods of studying special currents of homogenous events : candidate paper in physical-mathematical sciences. Tomsk, 2008.
- Nazarov A. A., Terpugov A. F. The theory of probabilities and accidental processes : textbook. Tomsk : NTL publishers, 2006.
- Gorbatenko A. E. Studying quasi-decomposable semi-Markov flow потока // The probability theory, mathematical statistics and appendix : journal of scientific article to an international science conference. Minsk, 2010. P. 53–59.
- Nazarov A. A., Moiseeva S. P. Methods of asymptotic analysis in the theory of mass services. Tomsk : NTL publishers, 2006.