Propagation of chaos for Hölder continuous interaction kernels via Glivenko-Cantelli

2016/08/09 by Thomas Holding, Holding, Thomas
Economics, Econometrics and Finance · Mathematics · #35Q83 #60H30 #82C31 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1608.02877

openalex publication_date 2016/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a new technique for establishing quantitative propagation of chaos for systems of interacting particles. Using this technique we prove propagation of chaos for diffusing particles whose interaction kernel is merely Hölder continuous, even at long ranges. Moreover, we do not require specially prepared initial data. On the way, we establish a law of large numbers for SDEs that holds over a class of vector fields simultaneously. The proofs bring together ideas from empirical process theory and stochastic flows.

Citations

• Mean Field Limit and Propagation of Chaos for Vlasov Systems with Bounded Forces
• Weak Well Posedness for Hypoelliptic Stochastic Differential Equation with Singular Drift: A Sharp Result
• Stochastic Hamiltonian flows with singular coefficients
• Degenerate SDE with Hölder-Dini Drift and Non-Lipschitz Noise Coefficient
• On the rate of convergence in Wasserstein distance of the empirical\n measure

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