Sur l'approximation de la distribution stationnaire d'une chaîne de Markov stochastiquement monotone

Some universal limits for nonhomogeneous birth and death processes

“…Estimates concerning the distance between truncated and infinite models for homogeneous BDP are presented in [9]. Some queueing applications of periodic BDP are given in [7].…”

On the Estimates of Average Characteristics of Some Birth and Death Processes

“…Putting d k = 2 k , k 0, we obtain α (t) = 3 − sin 2πt + 2 cos 2πt, α * = For t = 8, N = 40 we obtainĒ * ≈ 0, 2945 with accuracy 10 −4 . Figure 2 shows the graph of function φ(t), t ∈ [8,9] with accuracy 10 −5 ; the same picture shows φ * (t) for large t with accuracy 10 −4 . …”

“…(see, e.g., [2,[6][7][8][9]). Two important characteristics -limit mean and double mean -were introduced and studied for processes with periodic intensities in [1,[3][4][5].…”

A weak perturbation theory for approximations of invariant measures in M/G/1 model

“…The strong perturbation theory [13], requires that { P k } k≥1 converges to P in operator norm on B 1 . Unfortunately the convergence of P − P k 1 to 0 is a condition quite demanding, so it is not always satisfied, even in simple cases [5,24,25]. This is why we use the weak perturbation theory due to Keller and Liverani [14,16] which invokes the weakened convergence property…”

“…Kalashnikov and Rachev [12] have also studied the problem of the approximation of an infinite Markov chain, the main part of their work is oriented towards the uniform approximation of the initial chain by finite chains constructed by augmentation of the first column. Simonot [25] was examine the case of an infinite irreducible stochastic matrix, dominated by stochastically monotone chains, the rate of convergence of π k to π was derived in terms of Foster-Lyapounov condition. Tweedie [27] provided simple error bound in the case of geometrically ergodic chains, stochastically monotone chains, and those dominated by stochastically monotone chains.…”