Search results for "Kolmogorov equations"

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Qualitative Analysis of Differential, Difference Equations, and Dynamic Equations on Time Scales

2015

and Applied Analysis 3 thank Guest Editors Josef Dibĺik, Alexander Domoshnitsky, Yuriy V. Rogovchenko, Felix Sadyrbaev, and Qi-Ru Wang for their unfailing support with editorial work that ensured timely preparation of this special edition. Tongxing Li Josef Dibĺik Alexander Domoshnitsky Yuriy V. Rogovchenko Felix Sadyrbaev Qi-Ru Wang

Article SubjectDifferential equationlcsh:MathematicsApplied MathematicsFinite difference methodlcsh:QA1-939Stochastic partial differential equationNonlinear systemMultigrid methodKolmogorov equations (Markov jump process)Simultaneous equationsApplied mathematicsAnalysisNumerical partial differential equationsMathematicsAbstract and Applied Analysis
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Stationary and Initial-Terminal Value Problem for Collective Decision Making via Mean-Field Games

2017

Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, following some optimality criteria. The optimal transition rates are based on the players' knowledge of their current state and of the distribution of all the other players, thus introducing mean-field terms in the running and the terminal cost. The first contribution is a mean-field model that takes into account the macroscopic and the microscopic dynamics. The second contribution is the study of the mean-field equilibrium resulting from solving the initial-terminal value problem, involving the Kolmogorov equat…

Lyapunov function0209 industrial biotechnologyMathematical optimization010102 general mathematicsMarkov processContext (language use)02 engineering and technology01 natural sciencesTerminal valueNonlinear systemsymbols.namesake020901 industrial engineering & automationStability theoryKolmogorov equationssymbolsGames Mathematical model Markov processes Sociology Statistics Microscopy RobustnessApplied mathematicsLimit (mathematics)0101 mathematicsSettore MAT/09 - Ricerca OperativaMathematics
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