RESEARCH OF THE SEMI-MARKOVIAN PROCESS IN CONDITIONS OF LIMITEDLY RARE CHANGES IN ITS STATE

详细

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.

全文:

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.