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Dmitrii Silvestrov

Publications and source records attributed to Dmitrii Silvestrov.

8 recordsLinked to original sources
arXiv2019

Algorithms of Phase Space Reduction and Asymptotics of Hitting Times for Perturbed Semi-Markov Processes

The paper presents new asymptotic recurrent algorithms of phase space reduction for regularly and singularly perturbed semi-Markov processes. These algorithms give effective conditions of weak convergence for distributions and convergence of expectations for hitting times as well as recurrent formulas for computing the corresponding normalisation functions, Laplace transforms for limiting distributions and limits for expectations.

math.PR↗
arXiv2019

Perturbed Markov Chains and Information Networks

The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter $\varepsilon$. We give effective upper bounds for the rate of approximation for stationary distributions of unperturbed Markov chains by stationary distributions of perturbed Markov chains with regularised matrices of transition probabilities, asymptotic expansions for approximating stationary distributions with respect to damping parameter, as well as explicit upper bounds for the rate of convergence in ergodic theorems for $n$-step transition probabilities in triangular array mode, where perturbation parameter $\varepsilon \to 0$ and $n \to \infty$, simultaneously. The results of numerical experiments are also presented

math.PR↗
arXiv2016

Nonlinearly Perturbed Birth-Death-Type Models

Asymptotic expansions for stationary and conditional quasi-stationary distributions of nonlinearly perturbed birth-death-type semi-Markov models are presented. Applications to models of population growth, epidemic spread and population genetics are discussed.

math.PR↗
arXiv2016

Reward Algorithms for Semi-Markov Processes

New algorithms for computing power moments of hitting times and accumulated rewards of hitting type for semi-Markov processes. The algorithms are based on special techniques of sequential phase space reduction and recurrence relations connecting moments of rewards. Applications are discussed as well as possible generalisations of presented results and results of experimental studies.

math.PR↗
arXiv2016

Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. I

New algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on a special technique of sequential phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces. Asymptotic expansions are given in two forms, without and with explicit bounds for remainders.

math.PR↗