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Probabilistic and combinatorial techniques are often used for solving advanced problems. This book describes different probabilistic modeling methods and their applications in various areas, such as artificial intelligence, offshore platforms, social networks, and others. It aims to educate how modern probabilistic and combinatorial models may be created to formalize uncertainties; to train how new probabilistic models can be generated for the systems of complex structures; to describe the correct use of the presented models for rational control in systems creation and operation; and to demonstrate analytical possibilities and practical effects for solving different system problems on each life cycle stage.

Probabilities --- Periodicals.

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Probabilistic and combinatorial techniques are often used for solving advanced problems. This book describes different probabilistic modeling methods and their applications in various areas, such as artificial intelligence, offshore platforms, social networks, and others. It aims to educate how modern probabilistic and combinatorial models may be created to formalize uncertainties; to train how new probabilistic models can be generated for the systems of complex structures; to describe the correct use of the presented models for rational control in systems creation and operation; and to demonstrate analytical possibilities and practical effects for solving different system problems on each life cycle stage.

Probabilities --- Periodicals.

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The aim of this special issue is to publish original research papers that cover recent advances in the theory and application of stochastic processes. There is especial focus on applications of stochastic processes as models of dynamic phenomena in various research areas, such as queuing theory, physics, biology, economics, medicine, reliability theory, and financial mathematics. Potential topics include, but are not limited to: Markov chains and processes; large deviations and limit theorems; random motions; stochastic biological model; reliability, availability, maintenance, inspection; queueing models; queueing network models; computational methods for stochastic models; applications to risk theory, insurance and mathematical finance.

recursive formula --- rate of convergence --- asymptotic approximation --- parabolic equation --- processor heating and cooling --- compound poisson insurance risk model --- Koksma-Hlawka inequality --- phase-type service time distribution --- discrete-time Geo/D/1 queue --- lower record values --- Fourier-cosine series --- retrials --- state-dependent marked Markovian arrival process --- queuing network --- stochastic processes --- Laplace transform --- von-Neumann–Ulam scheme --- Monte Carlo method --- Lévy process --- Wiener–Poisson risk model --- queueing systems --- quasi-random sequences --- closed-form solution --- Cauchy problem --- product form --- estimation --- extreme order statistics --- guaranteed minimum death benefit --- valuation --- multidimensional birth-death process --- Markovian queueing models --- survival probability --- truncated distribution --- Markovian arrival process --- inhomogeneous continuous-time Markov chain --- measure of information --- option --- unbiased estimator --- matrix-geometric solution --- Dickson–Hipp operator --- Fourier transform --- multi-class arrival processes --- total precipitation volume --- one dimensional projection --- random sample size --- markovian arrival process --- cumulative inaccuracy --- mutual information --- Quasi-Birth-and-Death process --- limiting characteristics --- testing statistical hypotheses --- wet periods --- compound Poisson risk model --- time-dependent queue-length probability --- non-stationary --- equity-linked death benefits --- wireless telecommunication networks --- Fourier cosine series expansion --- impatience --- generalized Gerber–Shiu discounted penalty function --- quasi-Monte Carlo method --- expected discounted penalty function --- Nonparametric threshold estimation

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The aim of this Special Issue of Mathematics is to commemorate the outstanding Russian mathematician Vladimir Zolotarev, whose 90th birthday will be celebrated on February 27th, 2021. The present Special Issue contains a collection of new papers by participants in sessions of the International Seminar on Stability Problems for Stochastic Models founded by Zolotarev. Along with research in probability distributions theory, limit theorems of probability theory, stochastic processes, mathematical statistics, and queuing theory, this collection contains papers dealing with applications of stochastic models in modeling of pension schemes, modeling of extreme precipitation, construction of statistical indicators of scientific publication importance, and other fields.

continuous-time Markov chains --- non-stationary Markovian queueing model --- stability --- perturbation bounds --- forward Kolmogorov system --- threshold processing --- random samples --- long-term dependence --- mean-square risk estimate --- integrals and sums --- rates of convergence --- conditional law of large numbers --- conditional central limit theorem --- stochastic differential observation system --- nonlinear filtering problem --- state-dependent observation noise --- numerical filtering algorithm --- filtering given time-discretized observations --- stable approximation --- approximation accuracy --- Rényi theorem --- Kantorovich distance --- zeta-metrics --- Stein’s method --- stationary renewal distribution --- equilibrium transform --- geometric random sum --- characteristic function --- precipitation --- limit theorems --- statistical test --- generalized negative binomial distribution --- generalized gamma distribution --- asymptotic approximations --- extreme order statistics --- random sample size --- slowly varying --- monotony in the Zygmund sense --- class Γa(g) --- self-neglecting function --- convergence rates --- citation distribution --- Hirsch index --- geometric distribution --- Sibuya distribution --- geometrically stable distribution --- generalized Linnik distribution --- random sum --- transfer theorem --- multivariate normal scale mixtures --- heavy-tailed distributions --- multivariate stable distribution --- multivariate Linnik distribution --- generalized Mittag–Leffler distribution --- multivariate generalized Mittag–Leffler distribution --- stable distribution --- probability density function --- distribution function --- Hankel contours --- multivariate stable processes --- contour integrals --- fractional laplacian --- second order expansions --- high-dimensional --- low sample size --- Laplace distribution --- Student’s t-distribution --- pareto mixture distribution --- multiserver system --- uniform distance --- perfect simulation --- priority system --- marked Markov arrival process --- phase-type distribution --- change of the priority --- dispatching --- heterogeneous servers --- Markov decision process --- policy-iteration algorithm --- mean number of customers --- decomposable semi-regenerative process --- multiple power series distribution --- integral limit theorem --- local limit theorem --- Tauberian lemma --- R-weakly one-sided oscillation of the multiple sequence at infinity along the given multiple sequence --- pension schemes --- balance equation --- gross premium --- premium load --- lump sum --- defined contribution pension schemes --- decrement tables --- robustness --- minimax approach --- stable estimation

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Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia.

Research & information: general --- Mathematics & science --- Probability & statistics --- inhomogeneous continuous-time Markov chain --- weak ergodicity --- rate of convergence --- sharp bounds --- differential inequalities --- forward Kolmogorov system --- prefetching --- optimization --- Markov decision processes --- random trees --- Galton–Watson --- capacitance --- dirichlet boundary value problem --- monte carlo method --- unbiased estimator --- von-neumann-ulam scheme --- network evolution --- random graph --- multi-type branching process --- continuous-time branching process --- 2- and 3-interactions --- Malthusian parameter --- Poisson process --- life-length --- extinction --- queuing system --- elastic traffic --- inpatient claim --- non-stationary intensity --- convergence analysis --- bounds on the rate of convergence --- wireless network --- file transfer --- daily traffic profile --- blocking probability --- continuous-time ehrenfest model --- first-passage time densities --- proportional intensity functions --- asymptotic behaviors --- multi-server queueing model --- rating --- self-sufficient servers --- self-checkout --- assistants --- multi-dimensional Markov chains --- retrial queue --- negative customers --- resource heterogeneous queue --- asymptotic analysis --- discrete time functional filter --- optimal unbiased estimation --- steady state --- equilibrium arrivals --- one-server queueing system --- orbit --- retrials --- limit theorem --- sum of independent random variables --- random sum --- asymptotic expansion --- asymptotic deficiency --- kurtosis --- parameter estimation --- gamma-exponential distribution --- mixed distributions --- generalized gamma distribution --- generalized beta distribution --- method of moments --- cumulants --- asymptotic normality --- inhomogeneous continuous-time Markov chain --- weak ergodicity --- rate of convergence --- sharp bounds --- differential inequalities --- forward Kolmogorov system --- prefetching --- optimization --- Markov decision processes --- random trees --- Galton–Watson --- capacitance --- dirichlet boundary value problem --- monte carlo method --- unbiased estimator --- von-neumann-ulam scheme --- network evolution --- random graph --- multi-type branching process --- continuous-time branching process --- 2- and 3-interactions --- Malthusian parameter --- Poisson process --- life-length --- extinction --- queuing system --- elastic traffic --- inpatient claim --- non-stationary intensity --- convergence analysis --- bounds on the rate of convergence --- wireless network --- file transfer --- daily traffic profile --- blocking probability --- continuous-time ehrenfest model --- first-passage time densities --- proportional intensity functions --- asymptotic behaviors --- multi-server queueing model --- rating --- self-sufficient servers --- self-checkout --- assistants --- multi-dimensional Markov chains --- retrial queue --- negative customers --- resource heterogeneous queue --- asymptotic analysis --- discrete time functional filter --- optimal unbiased estimation --- steady state --- equilibrium arrivals --- one-server queueing system --- orbit --- retrials --- limit theorem --- sum of independent random variables --- random sum --- asymptotic expansion --- asymptotic deficiency --- kurtosis --- parameter estimation --- gamma-exponential distribution --- mixed distributions --- generalized gamma distribution --- generalized beta distribution --- method of moments --- cumulants --- asymptotic normality