惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

Microsoft Azure Blog
Microsoft Azure Blog
WordPress大学
WordPress大学
让小产品的独立变现更简单 - ezindie.com
让小产品的独立变现更简单 - ezindie.com
The Cloudflare Blog
U
Unit 42
D
Docker
Hugging Face - Blog
Hugging Face - Blog
博客园 - 聂微东
Recent Announcements
Recent Announcements
GbyAI
GbyAI
T
The Blog of Author Tim Ferriss
Last Week in AI
Last Week in AI
V
Visual Studio Blog
I
InfoQ
Google DeepMind News
Google DeepMind News
小众软件
小众软件
L
LangChain Blog
C
Check Point Blog
宝玉的分享
宝玉的分享
Martin Fowler
Martin Fowler
酷 壳 – CoolShell
酷 壳 – CoolShell
博客园 - 【当耐特】
J
Java Code Geeks
罗磊的独立博客

math.PR updates on arXiv.org

Visibility in the Boolean Model on Harmonic Manifolds Global estimates on the Brenier map Geodesics and Wandering Exponents in Brochette First-Passage Percolation State-dependent inverse-subordinator time changes of regenerative processes: Excursion structure and multiscale occupation-time limits Randomly twisted transfer operators and singular values statistics Generalized Bessel-Dunkl diffusions An almost sure invariance principle for the Takagi-van der Waerden class functions Central limit theorems for high dimensional lattice polytopes: cosmological polytopes Convergence rate estimates for semigroups and heat kernels associated with resistance forms Second-order Poincaré inequalities and localization on the Poisson space Maximum Probability of Independence in Transitive Matroids On global solutions to the semidiscrete stochastic heat equation The Poisson Tail Conjecture for primes in short intervals A Complete Spectral Analysis of the CEV Operator with Applications to Arbitrage Holographic functions and neural networks From Betting to Empirical Bernstein LIL Concentration of General Stochastic Approximation Under Heavy-Tailed Markovian Noise Pointwise Generalization in Deep Neural Networks Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors Wasserstein bounds for denoising diffusion probabilistic models via the Föllmer process A note on connections between the Föllmer process and the denoising diffusion probabilistic model Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equations A Fourier perspective on the learning dynamics of neural networks: from sample complexities to mechanistic insights Propagation of Chaos in Contextual Flow Maps Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixtures $α$-TCAV: A Unified Framework for Testing with Concept Activation Vectors Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model On the Limits of Latent Reuse in Diffusion Models State-of-art minibatches via novel DPP kernels: discretization, wavelets, and rough objectives
Fokker-Planck equations for McKean-Vlasov SDEs driven by ...
Saloua Labed, Nacira Agram, Bernt Oksendal · 2024-09-11 · via math.PR updates on arXiv.org

This paper investigates the probability distribution of solutions to McKean--Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst parameter H>1/2. Our main contribution is the derivation of the associated Fokker--Planck equation, which characterizes the time evolution of the law of the solution in a suitable distributional framework. Under mild assumptions, we show that the law-valued process is absolutely continuous in time and provide an explicit weak formulation of the corresponding fractional McKean--Vlasov Fokker--Planck equation. In the case where the law admits a density, we obtain a more explicit partial differential equation with time-dependent diffusion coefficients induced by the fractional noise. We further establish a fractional Feynman--Kac representation, linking the forward Fokker--Planck equation with a backward Kolmogorov equation for functionals of the solution process. This result extends the classical Feynman--Kac framework to mean--field dynamics driven by fractional Brownian motion. To illustrate the theory, we analyze several explicit examples, including the law of fractional Brownian motion itself and linear McKean--Vlasov fractional SDEs. These examples highlight how fractional noise and mean--field interactions jointly affect the probabilistic and analytic structure of the system.