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Measure-valued limits of interacting particle systems with k-nary interactions - I. One-dimensional limits
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On extensions of mollified Boltzmann and Smoluchowski equations to particle systems with a k-ary interaction
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Schrodinger operators with singular potentials and magnetic fields
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The rate of escape of stable Ornstein-Uhlenbeck processes and the scattering theory for thier perturbations
Small diffusion and fast dying out asymptotics for superprocesses as non-Hamiltonian quasiclassics for evolution equations
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A new path integral representation for the solutions of the Schrodinger, heat and stochastic Schrodinger equations
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Hydrodynamic limit of coagulation-fragmentation type models of k-nary interacting particles
Mean-field-game model for Botnet defense in cyber-security
We initiate the analysis of the response of computer owners to various offers of defence systems against a cyber-hacker (for instance, a botnet attack), as a stochastic game of a large number of interacting agents. We introduce a simple mean-field game that models their behavior. It takes into account both the random process of the propagation of the infection (controlled by the botner herder) and the decision making process of customers. Its stationary version turns out to be exactly solvable (but not at all trivial) under an additional natural assumption that the execution time of the decisions of the customers (say, switch on or out the defence system) is much faster that the infection rates.Department of Logistics and Maritime Studie
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