Note on nonlinear semigroups and free boundary problem for controlled Markov processes

Makiko Nisio

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This note contains a survey of recent results concerning asymptotic properties of Markov operators and semigroups. Some biological and physical applications are given.

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Nonlinear Markov processes in big networks

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Big networks express multiple classes of large-scale networks in many practical areas such as computer networks, internet of things, cloud computation, manufacturing systems, transportation networks, and healthcare systems. This paper analyzes such big networks, and applies the mean-field theory and the nonlinear Markov processes to constructing a broad class of nonlinear continuous-time block-structured Markov processes, which can be used to deal with many practical stochastic systems....

Accurate calculations of Stationary Distributions and Mean First Passage Times in Markov Renewal Processes and Markov Chains

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This article describes an accurate procedure for computing the mean first passage times of a finite irreducible Markov chain and a Markov renewal process. The method is a refinement to the Kohlas, Zeit fur Oper Res, 30, 197–207, (1986) procedure. The technique is numerically stable in that it doesn’t involve subtractions. Algebraic expressions for the special cases of one, two, three and four states are derived.Aconsequence of the procedure is that the stationary distribution of the...