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## ON CONSISTENCY OF BAYESIAN PARAMETER ESTIMATORS FOR A CLASS OF ERGODIC MARKOV MODELS

Reliability: Theory & Applications. 2022. Vol. 17. No. 4(71). P. 521-529.

A.I. Nurieva, A.Yu. Veretennikov

The consistency of the Bayesian estimation of a parameter is shown for a class of ergodic discrete Markov chains. J.L. Doob’s method was used, offered earlier for the i.i.d. situation. The result may be useful in the reliability theory for models with unknown parameters, in the risk management in financial mathematics, and in other applications.

Kashtanov V., Enatskaya N., Юрайт, 2017

The textbook has passed practical tests and written on the basis of the readable authors for many years. Presented in textbook materials give students orientation in the solution of many practical problems in a number of areas, constitute the initial level to obtain a broader and deeper education in the field of probability theory. The ...

Added: December 17, 2017

Gribkova N., Zitikis R., Mathematical Methods of Statistics 2017 Vol. 26 P. 267-281

The ‘beta’ is one of the key quantities in the capital asset pricing model (CAPM). In statistical language, the beta can be viewed as the slope of the regression line fitted to financial returns on the market against the returns on the asset under consideration. The insurance counterpart of CAPM, called the weighted insurance pricing ...

Added: February 28, 2020

Yanovskaya E. B., Dietzenbacher B., Mathematical Social Sciences 2022 P. 1-7

This paper introduces and studies the equal split-off set for cooperative games with nontransferable utility. We illustrate the new solution for the well-known Roth-Shafer examples and present two axiomatic characterizations based on different consistency properties on the class of exact partition games, i.e. the class of games where it intersects the core. ...

Added: December 5, 2022

Bulgakov S. A., Khametov V., Автоматика и телемеханика 2023 № 2 С. 122-149

The article aims to construct a solution for the problem of the optimal recovery (in the mean-square sense) of a measurable square-integrable (with respect to the Lebesgue measure) function defined on a finite-dimensional compact set. We justify the optimal recovery procedure for the aforementioned function observed at each point of the compact set with Gaussian ...

Added: November 27, 2020

Царев А. С., Хайров Э. М., Гайдамака Ю. В. et al., Системы и средства информатики 2021 Т. 31 № 2 С. 16-25

Industrial Internet of Things (IIoT) is one of the key features of Industry 4.0 that stands for a new approach to design industrial processes using the latest technological advances. However, before implementing new processes, it is necessary to understand the characteristics and limitations that arise due to technical complexity of the system. To solve this ...

Added: December 12, 2022

Minsk : [б.и.], 2022

This collection of papers includes proceedings of the Thirteenth International Conference "Computer Data Analysis and Modeling: Stochastics and Data Science" organized by the Belarusian State University and held in September 2022 in Minsk. Papers are reviewed by qualied researchers from Belarus and Russia. ...

Added: October 27, 2022

Khametov V., Bulgakov S. A., Управление большими системами: сборник трудов 2015 № 54 С. 45-65

The aim of the article is to construct a solution for the problem of the optimal recovery (in the mean-square sense) of a measurable square-integrable (with respect to the Lebesgue measure) function defined on a finite-dimensional compact set. We prove optimal recovery procedure and establish conditions of its unbiasedness and consistency. Furthermore, an ε^(1/2)-optimal stochastic recovery procedure is proposed and proved. ...

Added: March 9, 2016

Bezhaeva Z., Oseledets V. I., Обозрение прикладной и промышленной математики 2011 Т. 18 № 4 С. 622-623

Рассматривается стационарная марковская цепь с конечным алфавитом и неприводимой переходной матрицей. Скрытая марковская цепь возникает из марковской цепи при передаче через канал. Получена формула для энтропии скрытой марковской цепи. Эффективность формулы продемонстрирована на конкретных примерах. ...

Added: March 22, 2013

Кацев И. В., Yanovskaya E. B., Математическая теория игр и ее приложения 2009 Т. 1 № 1 С. 46-66

A collection of TU games solutions intermediate between the prekernel and the prenucleolus is considered. All these solutions
are Davis-Maschler consistent, symmetric and covariant. Each solution from the collection is parametrized by a positive integer k such that for all games with the number of players not greater than k, the solution for parameter k coincides
with ...

Added: March 20, 2014

Konakov V., Kozhina A., Menozzi S., / Cornell University. Series arXiv "math". 2016. No. 1506.08758v2.

We are interested in studying the sensitivity of diffusion processes or their approximations by Markov Chains with respect to a perturbation of the coefficients. As an important application, we give a first order expansion for the difference of the densities of a diffusion with H¨older coefficients and its approximation by the Euler scheme. ...

Added: July 1, 2015

Grabchak M., Kelbert M., Paris Q., Journal of Applied Probability 2020 Vol. 57 No. 1 P. 53-77

This article studies the expected occupancy probabilities on an alphabet. Unlike
the standard situation, where observations are assumed to be independent and identically
distributed (iid), we assume that they follow a regime switching Markov chain. For
this model, we 1) give finite sample bounds on the occupancy probabilities, and 2) provide
detailed asymptotics in the case where the underlying ...

Added: November 13, 2019

Konakov V., Woerner J., Mammen E., Bernoulli: a journal of mathematical statistics and probability 2014 Vol. 20 No. 2 P. 623-644

We assume that a high frequency Markov chain runs in the background on a very fine time grid but that it is only observed on a coarser grid. In this paper we show that under appropriate conditions the L1 distance between the joint distribution of the Markov chain and the distribution of the discretized diffusion ...

Added: November 13, 2013

Тулупьев А. Л., Sirotkin A., Вестник Санкт-Петербургского университета. Серия 1. Математика. Механика. Астрономия 2012 № 3 С. 63-72

The processing of probabilistically uncertain knowledge patterns in intellectual decision support systems falls into three kinds of probabilistic-logic inference, such as reconciliation, a priori and a posteriori inference. The paper presents formulae that allow for putting the process down in terms of matrix-vector language. ...

Added: March 25, 2014

Decrouez G. G., Robinson A., Risk Analysis: An International Journal 2013 Vol. 33 No. 12 P. 2142-2153

We propose a new modeling approach for inspection data that provides a more useful interpretation of the patterns of detections of invasive pests, using cargo inspection as a motivating example. Methods that are currently in use generally classify shipments according to their likelihood of carrying biosecurity risk material, given available historical and contextual data. Ideally, ...

Added: September 29, 2014

Kashtanov V., Kondrashova E. V., Надежность 2012 No. 1 (40) P. 68-83

The present paper analyses characteristics of an input flow controlled by Marcov chain. At the base of construction of the given flow rests the model of semi-Markov process. The paper has stated and proved the teorem about stationarity of an input flow controlled by Markov chain. In addition to that the theorem proved that in ...

Added: April 8, 2013

Dietzenbacher B., Kondratev A., Management Science 2023 Vol. 69 No. 6 P. 3319-3339

Given the ranking of competitors, how should the prize endowment be allocated? This paper introduces and axiomatically studies the prize allocation problem. We focus on consistent prize allocation rules satisfying elementary solidarity and fairness principles. In particular, we derive several families of rules satisfying anonymity, order preservation, and endowment monotonicity, which all fall between the ...

Added: September 7, 2022

Blank M., Moscow Mathematical Journal 2019 Vol. 19 No. 1 P. 37-50

Using ideas borrowed from topological dynamics and ergodic theory we introduce topological and metric versions of the recurrence property for general Markov chains. The main question of interest here is how large is the set of recurrent points. We show that under some mild technical assumptions the set of non-recurrent points is of zero reference measure. Necessary and ...

Added: October 8, 2019

Kashtanov V., Kondrashova E. V., Надежность 2012 № 1 (40) С. 52-68

The present paper analyses characteristics of an input flow controlled by Markov chain. At the base of construction of the given flow rests the model of semi-Markov process. The paper has stated and proved the theorem about stationarity of an input flow controlled by Markov chain. In addition to that the theorem proved that in ...

Added: February 25, 2013

Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016

The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...

Added: November 2, 2016

Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216

Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...

Added: December 4, 2017

Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253

Added: December 22, 2016

Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.

We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...

Added: September 29, 2019

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020