ON STRONG SOLUTIONS OF ITO'S EQUATIONS WITH σ ∈ Wd1 AND b ∈ Ld

• 成果类型: Article
• 署名作者: Krylov, N., V
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1525
• 发表日期: 2021
• 页码: 3142-3167
• 关键词: explicit formulas

摘要

We consider Ito uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in W-d,loc(1) and the drift in L-d. We prove the unique strong solvability for any starting point and prove that, as a function of the starting point, the solutions are Holder continuous with any exponent < 1. We also prove that if we are given a sequence of coefficients converging in an appropriate sense to the original ones, then the solutions of approximating equations converge to the solution of the original one.