Academic literature on the topic 'Hamilton-Jacobi-Bellman and Fokker-Planck equations'
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Journal articles on the topic "Hamilton-Jacobi-Bellman and Fokker-Planck equations"
Bensoussan, Alain, and Sheung Chi Phillip Yam. "Mean field approach to stochastic control with partial information." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 89. http://dx.doi.org/10.1051/cocv/2021085.
Full textCortés, Emilio, and J. I. Jiménez-Aquino. "Hamilton–Jacobi and Fokker–Planck equations for the harmonic oscillator." Physica A: Statistical Mechanics and its Applications 411 (October 2014): 1–11. http://dx.doi.org/10.1016/j.physa.2014.05.064.
Full textTottori, Takehiro, and Tetsuya J. Kobayashi. "Forward-Backward Sweep Method for the System of HJB-FP Equations in Memory-Limited Partially Observable Stochastic Control." Entropy 25, no. 2 (January 21, 2023): 208. http://dx.doi.org/10.3390/e25020208.
Full textBakaryan, Tigran, Rita Ferreira, and Diogo Gomes. "A potential approach for planning mean-field games in one dimension." Communications on Pure and Applied Analysis 21, no. 6 (2022): 2147. http://dx.doi.org/10.3934/cpaa.2022054.
Full textJiménez-Aquino, J. I., and Emilio Cortés. "Hamilton–Jacobi and Fokker–Planck equations for the harmonic oscillator in the inertial regime." Physica A: Statistical Mechanics and its Applications 422 (March 2015): 203–9. http://dx.doi.org/10.1016/j.physa.2014.12.012.
Full textMollai, Maedeh, and Seyed Majid Saberi Fathi. "An Application of the Madelung Formalism for Dissipating and Decaying Systems." Symmetry 13, no. 5 (May 6, 2021): 812. http://dx.doi.org/10.3390/sym13050812.
Full textКорниенко, Виктория Сергеевна, Владимир Викторович Шайдуров, and Евгения Дмитриевна Карепова. "A finite difference analogue of the “mean field” equilibrium problem." Вычислительные технологии, no. 4(25) (September 16, 2020): 31–44. http://dx.doi.org/10.25743/ict.2020.25.4.004.
Full textMoreno Trujillo, John Freddy. "Una nota introductoria a los juegos de campo medio. Teoría y algunas aplicaciones." ODEON, no. 22 (July 4, 2023): 159–78. http://dx.doi.org/10.18601/17941113.n22.06.
Full textAnnunziato, Mario, Alfio Borzì, Fabio Nobile, and Raul Tempone. "On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks." Applied Mathematics 05, no. 16 (2014): 2476–84. http://dx.doi.org/10.4236/am.2014.516239.
Full textFomin, Igor, and Sergey Chervon. "Exact and Slow-Roll Solutions for Exponential Power-Law Inflation Connected with Modified Gravity and Observational Constraints." Universe 6, no. 11 (October 29, 2020): 199. http://dx.doi.org/10.3390/universe6110199.
Full textDissertations / Theses on the topic "Hamilton-Jacobi-Bellman and Fokker-Planck equations"
Izydorczyk, Lucas. "Probabilistic backward McKean numerical methods for PDEs and one application to energy management." Electronic Thesis or Diss., Institut polytechnique de Paris, 2021. http://www.theses.fr/2021IPPAE008.
Full textThis thesis concerns McKean Stochastic Differential Equations (SDEs) to representpossibly non-linear Partial Differential Equations (PDEs). Those depend not onlyon the time and position of a given particle, but also on its probability law. In particular, we treat the unusual case of Fokker-Planck type PDEs with prescribed final data. We discuss existence and uniqueness for those equations and provide a probabilistic representation in the form of McKean type equation, whose unique solution corresponds to the time-reversal dynamics of a diffusion process.We introduce the notion of fully backward representation of a semilinear PDE: thatconsists in fact in the coupling of a classical Backward SDE with an underlying processevolving backwardly in time. We also discuss an application to the representationof Hamilton-Jacobi-Bellman Equation (HJB) in stochastic control. Based on this, we propose a Monte-Carlo algorithm to solve some control problems which has advantages in terms of computational efficiency and memory whencompared to traditional forward-backward approaches. We apply this method in the context of demand side management problems occurring in power systems. Finally, we survey the use of generalized McKean SDEs to represent non-linear and non-conservative extensions of Fokker-Planck type PDEs
GOFFI, ALESSANDRO. "Topics in nonlinear PDEs: from Mean Field Games to problems modeled on Hörmander vector fields." Doctoral thesis, Gran Sasso Science Institute, 2019. http://hdl.handle.net/20.500.12571/9808.
Full textLima, Lucas Fabiano. "A mean-field game model of economic growth : an essay in regularity theory." Universidade Federal de São Carlos, 2016. https://repositorio.ufscar.br/handle/ufscar/8902.
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
In this thesis, we present a priori estimates for solutions of a mean-field game (MFG) defined over a bounded domain Ω ⊂ ℝd. We propose an application of these results to a model of capital and wealth accumulation. In Chapter 1, an introduction to mean-field games is presented. We also put forward some of the motivation from Economics and discuss previous developments in the theory of differential games. These comments aim at indicating the connection between mean-field games theory, its applications and the realm of Mathematical Analysis. In Chapter 2, we present an optimal control problem. Here, the agents are supposed to be undistinguishable, rational and intelligent. Undistinguishable means that every agent is governed by the same stochastic differential equation. Rational means that all efforts of the agent is to maximize a payoff functional. Intelligent means that they are able to solve an optimal control problem. Once we describe this (stochastic) optimal control problem, we produce a heuristic derivation of the mean-field games system, which is summarized in a Verification Theorem; this gives rise to the Hamilton-Jacobi equation (HJ). After that, we obtain the Fokker-Plank equation (FP). Finally, we present a representation formula for the solutions to the (HJ) equation, together with some regularity results. In Chapter 3, a specific optimal control problem is described and the associated MFG is presented. This MFG is prescribed in a bounded domain Ω ⊂ ℝd, which introduces substantialadditional challenges from the mathematical view point. This is due to estimates for the solutionsat the boundary in Lp. The rest of the chapter puts forward two well known tips of estimates: theso-called Hopf-Lax formula and the First Order Estimate. In Chapter 4, the wealth and capital accumulation mean-field game model is presented. The relevance of studying MFG in a bounded domain then becomes clear. In light of the results obtained in Chapter 3, we close Chapter 4 with the Hopf-Lax formula, and the First Order estimates. Three appendices close this thesis. They gather elementary material on Stochastic Calculus and Functional Analysis.
Nesta dissertação são apresentadas algumas estimativas a priori para soluções de sistemas mean-field games (MFG), definidos em domínios limitados Ω ⊂ ℝd. Tais estimativas são aplicadas em um modelo mean-field específico, que descreve o acúmulo de riqueza e capital. No Capítulo 1, é apresentada uma breve introdução histórica sobre os mean-field games. Nesta introdução, exploramos sua relação com a teoria dos jogos, cujos alicerces foram construídos por economistas e matemáticos ao longo do século XX. O objetivo do capítulo é transmitir. No Capítulo 2, apresentamos um problema de controle ótimo em que cada agente é suposto ser indistinguível, racional e inteligente. Indistinguível no sentido de que cada um é governado pela mesma equação diferencial estocástica. Racional no sentido de que todos os esforços do agente são no sentido de maximizar um funcional de recompensa e, inteligente no sentido de que são capazes de resolver um problema de controle ótimo. Descreve-se este problema de controle ótimo, e apresenta-se a derivação heurística dos mean-field games; obtém-se através de um Teorema de Verificação, a equação de Hamilton-Jacobi (HJ) associada, e em seguida, obtémse a equação de Fokker-Planck. De posse destas equações, apresentamos alguns resultados preliminares, como uma fórmula de representação para soluções da equação de HJ e alguns resultados de regularidade. No Capítulo 3, descreve-se um problema específico de controle ótimo e apresenta-se a respectiva derivação heurística culminando na descrição de um MFG com condições não periódicas na fronteira; esta abordagem é original na literatura de MFG. O restante do capítulo é dedicado à exposição de dois tipos bem conhecidos de estimativas: a fórmula de Hopf-Lax e estimativa de Primeira Ordem. Uma observação relevante, é a de que o trabalho em obter-se estimativas a priori é aumentado substancialmente neste caso, devido ao fato de lidarmos com estimativas para os termos de fronteira com normas em Lp. ao leitor, as origens da Teoria Econômica contemporânea, que surgem à partir da utilização da Matemática na formulação e resolução de problemas econômicos. Tal abordagem é motivada principalmente pelo rigor e clareza da Matemática em tais circunstâncias. No Capítulo 4, apresenta-se o modelo de jogo do tipo mean-field de acúmulo de capital e riqueza, o que deixa claro a relevância do estudo dos MFG em um domínio limitado. À luz dos resultados obtidos no Capítulo 3, encerramos o Capítulo 4 com as estimativas do tipo Hopf-Lax e de Primeira Ordem. Três apêndices encerram o texto desta dissertação de mestrado; estes reúnem material elementar sobre Cálculo Estocástico e Análise Funcional.
Machado, Velho Roberto. "Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods." Diss., 2017. http://hdl.handle.net/10754/625444.
Full textConference papers on the topic "Hamilton-Jacobi-Bellman and Fokker-Planck equations"
Grover, Piyush. "Stability Analysis in Mean-Field Games via an Evans Function Approach." In ASME 2018 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/dscc2018-8926.
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