From the 1 of 7 linked papers with an AI index.
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Quantitative Propagation of Chaos and Fluctuations for Kinetic McKean--Vlasov SDEs with Singular Interaction Kernels
Zimo Hao, Xicheng Zhang, Xianliang Zhao
The paper establishes quantitative bounds on how particle systems approximate kinetic McKean–Vlasov stochastic differential equations with singular interaction kernels, and proves…
Kinetic SDEs with subcritical distributional drifts
Zikai Chen, Zimo Hao, Xicheng Zhang
In this paper we study the well-posedness of the kinetic stochastic differential equation (SDE) in driven by Brownian motion: $$\mathord{\rm d} X_t=V_t\mat…
SDEs with supercritical distributional drifts
Zimo Hao, Xicheng Zhang
Let . In this paper, we investigate the following stochastic differential equation (SDE) in driven by Brownian motion $$ {\rm d} X_t=b(t,X_t){\rm d} t+\sqr…
Heat kernel estimates for nonlocal kinetic operators
Haojie Hou, Xicheng Zhang
In this paper, we employ probabilistic techniques to derive sharp, explicit two-sided estimates for the heat kernel of the nonlocal kinetic operator $$ Î^{α/2}_v + v \cdot \nabla…
-convergence rate of EM schemes for invariant measures of supercritical stable SDEs
Peng Chen, Lihu Xu, Xiaolong Zhang +1
By establishing the regularity estimates for nonlocal Stein/Poisson equations under -order Hölder and dissipative conditions on the coefficients, we derive the -con…