# Optimal Hölder Continuity of SHE and SWE with Rough Fractional Noise

@article{Hong2016OptimalHC, title={Optimal H{\"o}lder Continuity of SHE and SWE with Rough Fractional Noise}, author={Jialin Hong and Zhihui Liu}, journal={arXiv: Probability}, year={2016} }

We mainly focus on the stochastic heat equation (SHE), i.e., L = ∂t − ∂xx, and the stochastic wave equation (SWE), i.e., L = ∂tt − ∂xx, with specified initial data. In the SHE case we impose u(0, x) = u0(x), while in the SWE case we further impose ut(0, x) = v0(x). There has been a widespread interest in Holder continuity result for random fields. This type of sample path regularity is a key property that is needed early

#### One Citation

Approximating Stochastic Evolution Equations with Additive White and Rough Noises

- Mathematics, Computer Science
- SIAM J. Numer. Anal.
- 2017

Optimal error estimates are obtained for the Galerkin approximations of stochastic evolution equations driven by an additive Gaussian noise which is temporally white and spatially fractional with Hurst index less than or equal to 1/2. Expand

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