McKean-Vlasov
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Related Articles from SNS
Explicit numerical approximations for McKean-Vlasov stochastic differential equations in finite and infinite time
arXiv:2401.02878v5 Announce Type: replace-cross Abstract: Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes the theory on the propagation of chaos in the $L^{q}$ sense.
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations with nonconstant diffusion
arXiv:2502.03205v3 Announce Type: replace Abstract: We introduce multilevel Picard (MLP) approximations for McKean--Vlasov stochastic differential equations (SDEs) with nonconstant diffusion coefficient. Under standard Lipschitz assumptions on the coefficients, we show that the MLP algorithm approximates the solution of the SDE in the $L^2$-sense without the curse of dimensionality. The latter means that its computational cost grows at most polynomially in both the dimension and the...
Multiscale Nudging: From Macroscopic Observations to Microscopic Dynamics
arXiv:2606.06809v1 Announce Type: new Abstract: We introduce a measure-based nudging framework for assimilating macroscopic observations into microscopic mean-field particle dynamics. The central difficulty is a representation mismatch: the forecast is a labeled particle system, while the observations specify only a smoothed, permutation-invariant density. To address this mismatch, we define the forecast-observation discrepancy as a quadratic functional on probability measures after applying...
Generative Drifting is Secretly Score Matching: a Spectral and Variational Perspective
Announce Type: replace Abstract: Generative Modeling via Drifting~\citep{deng2026drifting} has recently achieved state-of-the-art one-step image generation through a kernel-based drift operator, yet its success is largely empirical and its theoretical foundations remain poorly understood. We observe that \emph{under a Gaussian kernel, the drift operator is exactly a score difference on smoothed distributions}. This answers three questions left open in the original work: (1) whether a...
Kolmogorov equations for evaluating the boundary hitting of degenerate diffusion with unsteady drift
arXiv:2501.02729v5 Announce Type: replace Abstract: Jacobi diffusion is a representative diffusion process whose solution is bounded in a domain under certain drift and diffusion coefficient conditions. However, the process without such conditions has not been thoroughly investigated. We explore a Jacobi diffusion whose drift coefficient is affected by another deterministic process, causing the process to hit the boundary of a domain in finite time.
Multiscale Nudging: From Macroscopic Observations to Microscopic Dynamics
arXiv:2606.06809v1 Announce Type: cross Abstract: We introduce a measure-based nudging framework for assimilating macroscopic observations into microscopic mean-field particle dynamics. The central difficulty is a representation mismatch: the forecast is a labeled particle system, while the observations specify only a smoothed, permutation-invariant density. To address this mismatch, we define the forecast-observation discrepancy as a quadratic functional on probability measures after...