The Vlasov–Fokker–Planck–Dean–Kawasaki equation with correlated noise and bounded nonlocal interactions has a unique probabilistically strong renormalized kinetic solution for finite-mass, finite-entropy initial data.
Second order fractional mean-field sdes with singular kernels and measure initial data., 2302.04392
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Kinetic Langevin processes with pure-jump Lévy noise satisfy strong Feller, irreducibility, spectral gap, and exponential ergodicity in low-regularity settings, with densities and C0-semigroup properties for alpha-stable cases.
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Kinetic Theory with Fluctuations: Strong Well-Posedness of the Vlasov-Fokker-Planck-Dean-Kawasaki System
The Vlasov–Fokker–Planck–Dean–Kawasaki equation with correlated noise and bounded nonlocal interactions has a unique probabilistically strong renormalized kinetic solution for finite-mass, finite-entropy initial data.
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On some topological and spectral properties of kinetic Langevin processes driven by L{\'e}vy noises
Kinetic Langevin processes with pure-jump Lévy noise satisfy strong Feller, irreducibility, spectral gap, and exponential ergodicity in low-regularity settings, with densities and C0-semigroup properties for alpha-stable cases.