A Model for Network Virus Protection Based on Regenerative Process

Yu. Grishunina; L. Manita

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A Model for Network Virus Protection Based on Regenerative Process

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 of failure of any of the computers (non-
scheduled emergent reinstalling) or at scheduled time moments. We consider a
maximization problem of an average unit income. The cumulative distribution function (CDF)
of the scheduled intervals between complete OS reinstallings is considered as a control. We
prove that the optimal CDF has to be degenerate, ie, it is localized at a point τ τ

Language: English

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Keywords: Laplace transform преобразование Лапласа Virus Propagation Regenerative process Average unit profit Регенерирующий процесс средний удельный доход

In book

Analytical and computational methods in probability theory and its applications (ACMPT-2017). Proceedings of the International Scientific Conference

M.: RUDN, 2017.

Точное решение одного функционально-дифференциального уравнения параболического типа с помощью теории полугрупп и некоторые его применения

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

Fast and modular regularized topic modelling 21st Conference of Open Innovations Association, FRUCT 2017; Helsinki; Finland; 6 November 2017 до 10 November 2017; Номер категорииCFP1767Z-ART; Код 134240

Vorontsov K. V., Kochedykov D., Apishev M. et al., IEEE Computer Society, 2017.

Topic modelling is an area of text mining that has been actively developed in the last 15 years. A probabilistic topic model extracts a set of hidden topics from a collection of text documents. It defines each topic by a probability distribution over words and describes each document with a probability distribution over topics. In ...

Added: December 6, 2019

Limit Distributions in Stochastic Networks with Message-Passing Synchronization

Manita A., , in: Analytical and Computational Methods in Probability TheoryVol. 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

Optimal Antivirus Protection Strategy in Computer Networks

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

Added: July 2, 2018

Optimal Antivirus Protection Strategy in Computer Networks

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

Added: December 22, 2017

Generalized Post–Widder inversion formula with application to statistics

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

Stochastic Models of Virus Propagation In Computer Networks: Algorithms of Protection and Optimization

Yu. Grishunina, L. Manita, Lobachevskii Journal of Mathematics 2017 Vol. 38 No. 5 P. 906–909

We propose a new mathematical model of virus spreading over local area networks. We define a cost functional and consider a maximization problem for the average income given by the computer network per unit time. ...

Added: September 2, 2017

Statistical inference for time-changed Lévy processes via Mellin transform approach

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

Telegraph process in the bounded domain with absorbing lower boundary and reflecting with delay upper boundary

Pospelov I. G., Radionov S., / 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