Nonlinear Markov Processes and Kinetic Equations

By Vassili N. Kolokoltsov. 2010

320 citations recorded by the source corpus.

Subfields: Mathematical Physics, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2c31a7746bb6fa21b2c7d2aa16e0005ee875e610

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Citations in the corpus

Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions (2021, background): “Yet another powerful approach to quantitative propagation of chaos emerged recently, based on semigroup analysis, stemming from the important recent work [57] (see also [42] for related ideas).”
A mean-field limit for certain deep neural networks (2019, background): “More general nonlinear Markov processes are surveyed in Kolokoltsov’s book [13].”
On Ergodic Properties of Nonlinear Markov Chains and Stochastic McKean--Vlasov Equations (2013, background): “. These processes were introduced by H.P. McKean [11] to model plasma dynamics. Later nonlinear Markov processes were studied by a number of authors, let us mention here the books of V.N. Kolokoltsov [9] and of A.-S. Sznitman [16]. These processes arise naturally in the study of the limit behavior o”
Kac’s program in kinetic theory (2011, methodology): “After we had finished writing our paper, we were told about the recent book [44] by Kolokoltsov.”
Mean Field Analysis of Deep Neural Networks (2019, background): “Similarly to the general results of [34], νt,(C1 ◦ ,.”
Nonlinear Markov Games on a Finite State Space (Mean-field and Binary Interactions) (2012, methodology): “For the introduction to nonlinear Markov processes we refer to (Kolokoltsov, 2007, 2010) and references therein, or, for more physical point of view, to (Frank, 2008) or (Zak, 2002).”
Mean Field Analysis of Neural Networks: A Law of Large Numbers (2018, background): “1), \= \mu \cdot , is associated to the nonlinear random process Zt (see, for example, [29]) satisfying the random ordinary differential equation D ow nl oa de d 09 /0 4/ 20 to 8 0.”
Mean Field Games Models—A Brief Survey (2013, methodology): “Further developments, using the theory of nonlinear Markov processes were obtained in [65, 66], and [64] (see also the monograph [63]), and using PDE methods in [11].”
The Master Equation and the Convergence Problem in Mean Field Games (2015, result): “It is worth mentioning that similar ideas have been explored by Kolokoltsov in the monograph [39] and developed, in the McKean-Vlasov framework, in the subsequent works [40] and [41] in collaboration with his coauthors.”