Degenerate SDEs in Hilbert Spaces with Rough Drifts

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.

25 pages

Cited by in corpus (2)

• Degenerate SDE with Hölder-Dini Drift and Non-Lipschitz Noise Coefficient
• Harnack and Shift Harnack Inequalities for Degenerate (Functional) SPDEs with Singular Drifts