Joint distributions of synchronization models
We consider Markov models of multicomponent systems with synchronizing interaction. Under natural regularity assumptions about the message routing graph, they have nice longtime behavior. We are interested in limit probability laws related to the steady state viewed from the center-of-mass coordinate system.
, , in : Analytical and Computational Methods in Probability Theory. Vol. 10684: Analytical and Computational Methods in Probability Theory.: Berlin : Springer, 2017. P. 347-360.
We consider Markov models of multicomponent systems with synchronizing interaction. Under natural regularity assumptions about the message routing graph, they have nice longtime behavior. We are interested in limit probability laws related to the steady state viewed from the center-of-mass coordinate system. ...
Added: July 16, 2018
, Fractional Calculus and Applied Analysis 2019 Vol. 22 No. 3 P. 543-600
This paper aims at unifying and clarifying the recent advances in the analysis of the fractional and generalized fractional Partial Diﬀerential Equations of Caputo and Riemann-Liouville type arising essentially from the probabilistic point of view. This point of view leads to the path integral representation for the solutions of these equations, which is seen to ...
Added: November 14, 2019
, , Journal of Physics: Conference Series 2021 Vol. 1740 No. 1 P. 1-6
The classical Hegselmann-Krause opinion dynamics model is known for the simplicity of its interaction rules and for the striking complexity of its collective behavior observed in computer simulations. The nonlinearity of the dynamics makes an analytical study of the model a very hard task. Recently there is some interest in introducing a random noise in ...
Added: June 23, 2021
, , Journal of Functional Analysis 2012 Vol. 263 P. 248-303
We construct a four-parameter family of Markov processes on infinite Gelfand–Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov process on the infinite-dimensional boundary of the Gelfand–Tsetlin graph or, equivalently, the space of extreme characters of the infinite-dimensional unitary group U(∞). The process has a ...
Added: February 25, 2013
, , , Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 2015 Vol. 471 P. 1-19
Added: June 22, 2016
, , , , in : Dynamical Systems, Differential Equations and Applications. : AIMS, 2016. P. 132-141.
Added: June 22, 2016
, , , Applicable Analysis 2019 Vol. 98 No. 1-2 P. 217-231
The goal of the paper is to describe the large time behaviour of a symmetric diffusion in a high-contrast periodic environment and to characterize the limit process under the diffusive scaling. We consider separately the C_0 and L^2 settings. ...
Added: December 5, 2020
Risk-based availability modelling and reputation management on fault tolerant cloud computing systems
, , International Journal of Internet Technology and Secured Transactions 2019 Vol. 1 No. 2 P. 37-56
This paper exhibits a risk-based philosophy in cloud computing to estimate ideal quality and maintenance which maximise the high availability of cloud administration infrastructure. The procedure is confined into two stages: 1) accessibility displaying the cloud; 2) hazard based assessment. The projected procedure is practical to the healthcare scheme using Markov chain process. The proposed ...
Added: November 24, 2021
, Функциональный анализ и его приложения 2016 Т. 49 № 4 С. 61-75
Ранее А. М. Бородин и автор построили 4-параметрическое семейство марковских процессов на дуальном объекте к бесконечномерной унитарной группе. Основной новый результат состоит в том, что эти процессы являются пределами скачкообразных процессов на дуальных объектах к растущим компактным унитарным группам. ...
Added: December 29, 2016
An Empirical Analysis of Growth and Consolidation in Banking: A Markovian Approach for the case of Russia
, , International Journal of Computational Economics and Econometrics 2014 Vol. 4 No. 1/5 P. 112-129
This paper represents an empirical examination of the process of banks' growth in Russia during 2004-2010 years. A Stochastic process of growth is modeled by Markov chain theory. Elements in the transition matrices of Markov Chain are the transition probabilities that provide a plausible estimate of how the banking system structure changes from one period ...
Added: April 6, 2014
, Динамика сложных систем 2012 Т. 6 № 4 С. 17-20
The article presents the results of the task of algorithmization political model «Power - civil society» with the use of the apparatus of the theory of Markov processes and equations Foker-Planck - Kolmogorov. The solution of this problem is based on the use of analogies drawn from the study of natural and other objects, in ...
Added: February 19, 2013
Dirichlet’s and Thomson’s Principles for Non-selfadjoint Elliptic Operators with Application to Non-reversible Metastable Diffusion Processes
, , , Archive for Rational Mechanics and Analysis 2019 Vol. 231 No. 2 P. 887-938
We present two variational formulae for capacity in the context of non-selfadjoint elliptic operators. The minimizers of these variational problems are expressed as solutions of boundary-value elliptic equations. We use these principles to provide a sharp estimate for the transition times between two different wells for non-reversible diffusion processes. This estimate permits us to describe ...
Added: October 3, 2018
, Queueing Systems 2014 Vol. 76 No. 2 P. 149-180
We consider a stochastic model of clock synchronization in a wireless network of N sensors interacting with one dedicated accurate time server. For large N we find an estimate of the final time sychronization error for global and relative synchronization. The main results concern the behavior of the network on different timescales tN→∞ , N→∞ ...
Added: February 4, 2015
, , Mathematical Methods of Statistics 2016 Vol. 25 No. 3 P. 207-218
A new result on stability of an optimal nonlinear filter for a Markov chain with respect to small perturbations on every step is established. An exponential recurrence of the signal is assumed. ...
Added: October 16, 2016
, , Journal of Physics: Conference Series 2018 Vol. 955 No. 012038 P. 1-6
We propose new deterministic and stochastic models for synchronization of clocks in nodes of distributed networks. An external accurate time server is used to ensure convergence of the node clocks to the exact time. These systems have much in common with mathematical models of opinion formation in multiagent systems. There is a direct analogy between ...
Added: May 19, 2018
, , Логистика и управление цепями поставок 2013 Т. 57 № 4 С. 65-70
The article covers issues of effectiveness of working capital management of a trading enterprise on the basis of the automated planning. This uses the logistic approach to the formation of a management strategy, providing the maximum win with minimal losses. To this end, they have developed a functional model of the process of planning of ...
Added: November 23, 2013
, , , Journal of Applied Probability 2014 Vol. 51 No. 3 P. 837-857
The paper deals with nonlinear Poisson neuron network models with bounded memory dynamics, which can include both Hebbian learning mechanisms and refractory periods. The state of the network is described by the times elapsed since its neurons fired within the post-synaptic transfer kernel memory span, and the current strengths of synaptic connections, the state spaces ...
Added: September 29, 2014
, , On convergence rate for homogeneous Markov chains / Cornell University. Series "Working papers by Cornell University". 2019.
New convergence rate asymptotic bound for a class of homogeneous Markov chains is established. ...
Added: November 14, 2019
, , in : Probability and Statistical Physics in St. Petersburg. Vol. 91: Proceedings of Symposia in Pure Mathematics.: American Mathematical Society, 2016. P. 373-394.
We discuss the construction of certain infinite-dimensional continuous time Markov processes, based on the use of intertwined Markov semigroups. ...
Added: February 21, 2017
, Markov dynamics on the dual object to the infinite-dimensional unitary group / Cornell University. Series math "arxiv.org". 2013. No. 1310.6155.
These are notes for a mini-course of 3 lectures given at the St. Petersburg School in Probability and Statistical Physics (June 2012). My aim was to explain, on the example of a particular model, how ideas from the representation theory of big groups can be applied in probabilistic problems. The material is based on the joint paper arXiv:1009.2029 by ...
Added: November 16, 2013
Стохастическая модель потока власти политологической системы «Власть – гражданское общество» Стохастическая модель потока власти политологической системы «Власть – гражданское общество» Стохастическая модель потока власти политологической системы «Власть – гражданское общество»
, Качество Инновации Образование, РФ.Москва.Европейский центр по качеству 2014 № 11 С. 61-66
The article presents the results of stochastic modeling of flow of power in a hierarchical structure of the political model of Government - civil society using the apparatus of the equations of Fokker-Planck-Kolmogorov equation. These results are a further development of the well-known mathematical implementation of the General scheme of the system "power-society"that describes the ...
Added: March 14, 2015
, SIAM Journal on Control and Optimization 2016 Vol. 54 No. 5 P. 2629-2649
The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a model game. The dynamics of the model game differs from the original one. The general result applied ...
Added: April 17, 2020
, , , Optimal Control Applications and Methods 2019 P. 1-21
Using the tools of the Markov Decision Processes, we justify the dynamic programming approach to the optimal impulse control of deterministic dynamical systems. We prove the equivalence of the integral and diﬀerential forms of the optimality equation. The theory is illustrated by an example from mathematical epidemiology. The developed methods can be also useful for ...
Added: February 27, 2020