Semi-markov processes and their applications

Reward Algorithms for Semi-Markov Processes

“…We refer to works by Korolyuk et al (1974), Kovalenko (1975), Turbin (1976, 1978), Courtois (1977), Silvestrov (1980b), Anisimov et al (1987), Ciardo et al (1990), Kovalenko et al (1997), and Korolyuk and Korolyuk (1999), Limni-os andOprişan (2001, 2003), Barbu et al (2004), Zhang (2005, 2013), Manca (2006, 2007), Anisimov (2008), Gyllenberg and Silvestrov (2008), , and Papadopoulou (2013).…”

Chebyshev approximation of the distribution function of nonnegative random variables

“…The conditions for convergence of (21) to the exponential distribution are established in [3]. This result has been generalized in [4][5][6][7][8][9] by abandoning the assumption of identically distributed and independent summands in (20), and also by estimating the accuracy of the exponential distribution. Upper and lower bounds have been obtained [5,10,11] on the distribution function Oe(z), and also metric bounds [12,13] of the form #(Or(z), I --exp( --z)) < Ce, where # are some distances in the set of distribution functions, C > 0 are known constants.…”

Limit Theorems for Queuing Systems with Regenerative Doubly Stochastic Input Flow*

“…and {λ k , λ k < C, k 0}. It is known (see, e.g., [7]) that the distribution of U (t) is defined by two matrixes P = (p ij ) and G = (G ij (x)). The first matrix consists of transition probabilities from state (i) to state (j), and the second one consists of distribution functions of the sojourn time in the state i = 0, 1, 2 .…”