MCKEAN-VLASOV EQUATIONS
A Stochastic Particle Method with Random Weights for the Computation of Statistical Solutions of McKean-Vlasov Equations. Part II: Convergence Rate of The Method
... Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex France Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - [r] ...
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Diffusive processes on the Wasserstein space : coalescing models, regularization properties and McKean-Vlasov equations
... Le chapitre I propose une construction alternative, par approximations lisses, du sys- tème de particules défini par Konarovskyi et von Renesse, et appelé ci-après modèle coalescent. Le modèle coalescent est un processus ...
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A Stochastic Particle Method with Random Weights for the Computation of Statistical Solutions of McKean-Vlasov Equations. Part I: Foundation of the Method and Empirical Evidence
... Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex France Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - [r] ...
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Infinite-dimensional regularization of McKean-Vlasov equation with a Wasserstein diffusion
... L 1 (R); it is a subset of the space C 0 (R) of continuous functions vanishing at infinity. II.2 Definition of the notion of solution Let us consider a new model, with the purpose to make a link between the results ...
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Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications *
... The above control formulation of stochastic McKean-Vlasov equations provides a uni- fied framework for some important classes of control problems. In particular, it is motivated in particular by the ...
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Global solvability of a networked integrate-and-fire model of McKean-Vlasov type
... of McKean-Vlasov-type, since the process (X t ) t > 0 depends on the distribution of the solution ...to McKean-Vlasov equations and propagation of chaos, such as those presented by ...
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Control of McKean-Vlasov systems and applications
... time McKean-Vlasov equations requires more technicalities and mathematical tools, and is under current ...time McKean-Vlasov stochastic differential ...
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A VARIATIONAL SHEATH MODEL FOR GYROKINETIC VLASOV-POISSON EQUATIONS
... [29] E. Lieb and M. Loss. Analysis (2nd version). Grad. Stu. in Math. 14. Amer. Math. Soc., 2001. [30] G. Manfredi and D. Coulette. Kinetic simulations of the Chodura Debye sheath for magnetic fields with grazing ...
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Invariant measures of the 2D Euler and Vlasov equations
... Euler equations (please see [19, 22, 27] and references therein for recent developments of the kinetic theory of ...Euler equations or of the Vlasov equations with usual smooth initial ...
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White-noise driven conditional McKean-Vlasov limits for systems of particles with simultaneous and random jumps
... Abstract: We study the convergence of N particle systems described by SDEs driven by Brownian motion and Poisson random measure, where the coefficients depend on the empirical measure of the system. Every particle jumps ...
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PARTICLE-IN-WAVELETS SCHEME FOR THE 1D VLASOV-POISSON EQUATIONS
... R´ esum´ e. L’objectif de ce travail est de proposer un nouveau sch´ ema num´ erique, appel´ e particle-in- wavelets, pour r´ esoudre les ´ equations de Vlasov-Poisson, et de le tester dans le cas le plus ...
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McKean Feynman-Kac probabilistic representations of non-linear partial differential equations
... 3 McKean Feynman-Kac representations for non-conservative and non- linear PDEs The idea of generalizing MSDEs to MFKEs ...MFKE equations is that the probabilistic representation involves the past of the ...
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Fokker-Planck equations with terminal condition and related McKean probabilistic representation
... differential equations (PDEs) are well-posed if the initial condition is ...a McKean type equation corresponding to the time-reversal dynamics of a diffusion ...
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Randomized dynamic programming principle and Feynman-Kac representation for optimal control of McKean-Vlasov dynamics
... the McKean-Vlasov control problem, and its continuity ...randomized McKean-Vlasov control problem and we prove the fundamental equivalence result between V and V R (Theorem ...randomization ...
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On the well-posedness of a class of McKean Feynman-Kac equations
... X j=1 ∂ j (b 0,j (t, ·)ϕ(·))(x). (3) When Λ = 0, the above equation is a non-linear Fokker-Planck equation, it is conservative and it is known that, under mild assumptions, it describes the dynamics of the marginal prob- ...
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Forward-Backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics
... to McKean- Vlasov dynamics and give sufficient conditions for existence of an optimal ...Differential Equations (FBSDEs for short) where the marginal distributions of the solutions appear in the ...
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Geometric Particle-in-Cell methods for the Vlasov-Maxwell equations with spin effects
... spin Vlasov equation, coupled to Maxwell’s equations, constitutes a viable mean-field model where the electron orbital motion is treated classically, while the spin is a fully quantum variable (Hurst et ...
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Global existence of solutions for the coupled Vlasov and Navier-Stokes equations
... fluid equations are coupled through a drag term (which depends on both the fluid macroscopic quantities, and the probability density function and its variables), but not through the volume fraction occupied by the ...
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Particle system algorithm and chaos propagation related to non-conservative McKean type stochastic differential equations
... process X, starting at time t. Based on that idea, many judicious numerical schemes have been proposed by [9, 14]. However, all those rely on computing recursively conditional expectation functions which is known to be ...
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Numerical simulation of ECRIPAC plasma behaviour with Vlasov equations including electron and collective effects
... A 611 Vlasov code using the “particle method” was dcvelopped to simulate the electron heating process, the plasma compression and the energy transfer from electrons to io[r] ...
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