Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients

2014/07/22 by Longjie Xie, Xicheng Zhang, Xie, Longjie +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #60H10 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1407.5834

openalex publication_date 2014/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients with respect to the starting point. Moreover, we also study the strong Feller property and the irreducibility of the associated diffusion semigroup.

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• Large-Time Analysis of the Langevin Dynamics for Energies Fulfilling Polyak-Łojasiewicz Conditions

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