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## Limit Distributions in Stochastic Networks with Message-Passing Synchronization

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.

### In book

Vol. 10684: Analytical and Computational Methods in Probability Theory. , Berlin : Springer, 2017

A.Manita, , in : Analytical and computational methods in probability theory and its applications (ACMPT-2017). Proceedings of the International Scientific Conference. : M. : RUDN, 2017. P. 644-648.

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: November 14, 2017

Grishunina Y., Manita L., , in : Analytical and Computational Methods in Probability Theory. Vol. 10684: Analytical and Computational Methods in Probability Theory.: Berlin : Springer, 2017. P. 75-82.

We construct a mathematical model of anti-virus protection of local area networks. The model belongs to the class of regenerative processes. To protect the network from the external attacks of viruses and the spread of viruses within the network we apply two methods: updating antivirus signatures and reinstallings of operating systems (OS). Operating systems are ...

Added: July 2, 2018

Yu. Grishunina, L. Manita, , in : Analytical and computational methods in probability theory and its applications (ACMPT-2017). Proceedings of the International Scientific Conference. : M. : RUDN, 2017. P. 80-84.

We construct a mathematical model of anti-virus protection of local area networks. The
model belongs to the class of regenerative processes. To protect the network from the
external attacks of viruses and the spread of viruses within the network we apply two
methods: updating antivirus signatures and reinstallings of operating systems (OS).
Operating systems are reinstalled in the case ...

Added: June 20, 2018

Manita A., Manita L., 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

Molchanov S., Bogachev L., Derfel G., Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 2015 Vol. 471 P. 1-19

Added: June 22, 2016

Borodin A., Olshanski G., 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

Molchanov S., Bogachev L., Derfel G., , in : Dynamical Systems, Differential Equations and Applications. : AIMS, 2016. P. 132-141.

...

Added: June 22, 2016

Grishunina Y., Manita L., Lecture Notes in Computer Science 2017 Vol. 10684 P. 75-82

We construct a mathematical model of anti-virus protection of local area networks. The model belongs to the class of regenerative processes. To protect the network from the external attacks of viruses and the spread of viruses within the network we apply two methods: updating antivirus signatures and reinstallings of operating systems (OS). Operating systems are ...

Added: December 22, 2017

Bolychev A., Manita A., 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

Pospelov I. G., Radionov S., Telegraph process in the bounded domain with absorbing lower boundary and reflecting with delay upper boundary / Cornell University. Series arXiv "math". 2015. No. 1509.06945.

We study the asymmetric one-dimensional telegraph process in the bounded domain. Lower boundary is absorbing and upper boundary is reflecting with delay. Point stays in the upper boundary until switch of regime occurs. We obtain the distribution of this process in terms of Laplace trasforms ...

Added: October 22, 2015

Kolokoltsov V., 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

Averboukh Y., 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

Semin V. G., 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

Tumanov M., Piunovskly A., Plakhov A., 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

Belomestny D., Mai H., Schoenmakers J., Journal of Mathematical Analysis and Applications 2017 No. 455 P. 89-104

In this work we derive an inversion formula for the Laplace transform of a density observed on a curve in the complex domain, which generalizes the well known Post– Widder formula. We establish convergence of our inversion method and derive the corresponding convergence rates for the case of a Laplace transform of a smooth density. ...

Added: September 22, 2017

Belomestny D., Schoenmakers J., Stochastic Processes and their Applications 2016 Vol. 126 No. 7 P. 2092-2122

Given a Lévy process (Lt)t≥0 and an independent nondecreasing process (time change) (T(t))t≥0, we consider the problem of statistical inference on T based on low-frequency observations of the time-changed Lévy process LT(t). Our approach is based on the genuine use of Mellin and Laplace transforms. We propose a consistent estimator for the density of the increments of T in a stationary regime, derive its convergence ...

Added: May 4, 2016

Penikas H. I., Anastasia Petrova, 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

Landim C., Mariani M., Seo I., 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

Yampolsky S., Шаламов А. С., 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

Рассадин А. Э., Огарёв-Online 2022 № 14 Статья 8

In this paper, the Cₒ-semigroup operator is constructed, the infinitesimal generator of which is a linear combination of the diffusion-thermal conductivity operator and the spatial inversion operator on a straight line. The general properties of the evolution of functions defining initial conditions under the action of such an operator are discussed. It is shown that ...

Added: December 2, 2022

Semin V. G., 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

Decrouez G. G., Borovkov K., Gilson M., 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

Olshanski G., , 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

Olshanski G., 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