Sharp space-time regularity of the solution to stochastic heat equation driven by fractional-colored noise

@article{Herrell2018SharpSR,
  title={Sharp space-time regularity of the solution to stochastic heat equation driven by fractional-colored noise},
  author={Rande K. Herrell and Renming Song and Dongsheng Wu and Yimin Xiao},
  journal={Stochastic Analysis and Applications},
  year={2018},
  volume={38},
  pages={747 - 768}
}
Abstract In this article, we study the following stochastic heat equation where is the generator of a Lévy process X in B is a fractional-colored Gaussian noise with Hurst index in the time variable and spatial covariance function f which is the Fourier transform of a tempered measure After establishing the existence of solution for the stochastic heat equation, we study the regularity of the solution in both time and space variables. Under mild conditions, we establish the exact uniform… 
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