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From Stochastic Hamiltonian Systems to Stochastic Compressible Euler Equation
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abstract
We study a stochastic Hamiltonian system of $N$ particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical measures associated to the position and velocity of the system converge to the solutions of stochastic compressible Euler equations in the limit as the particle number tends to infinity. Moreover, we quantify the distance between particles and the limit in suitable Sobolev norm.
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Quantitative particle approximation of nonlinear stochastic Fokker-Planck equations with singular kernel
The paper derives explicit N^{-κ} error bounds for the mollified empirical measure of moderately interacting particles with common noise, and proves local strong well-posedness of the limiting stochastic Fokker-Planck...
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