Degenerate SDEs in Hilbert Spaces with Rough Drifts

2015/01/17 by Feng-Yu Wang, Xicheng Zhang, Wang, Feng-Yu +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1501.04150

25 pages

arxiv created 2015/01/17 · arxiv updated 2015/01/20

Abstract

The existence and uniqueness of mild solutions are proved for a class of degenerate stochastic differential equations on Hilbert spaces where the drift is Dini continuous in the component with noise and Hölder continuous of order larger than \ff 2 3 in the other component. In the finite-dimensional case the Dini continuity is further weakened. The main results are applied to solve second order stochastic systems driven by space-time white noises.

Related

• Degenerate SDE with Hölder-Dini Drift and Non-Lipschitz Noise Coefficient
• Gradient Estimates and Applications for SDEs in Hilbert Space with Multiplicative Noise and Dini Continuous Drift
• Strong Uniqueness of Degenerate SDEs with Hölder diffusion coefficients
• Weak uniqueness by noise for singular stochastic PDEs
• Well-posedness for SDEs driven by different type of noises