Degenerate SDEs in Hilbert Spaces with Rough Drifts

Feng-Yu Wang; Xicheng Zhang

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arXiv · 1501.04150

Degenerate SDEs in Hilbert Spaces with Rough Drifts

Feng-Yu Wang·Xicheng Zhang

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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 H\"older 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.

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Feng-Yu Wang, Xicheng Zhang. 2015-01-17. Degenerate SDEs in Hilbert Spaces with Rough Drifts. https://arxiv.org/abs/1501.04150

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