### Abstract

We consider the initial boundary value problem of the non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random noises. The space boundary is Lipschitz, and we impose nonzero condition on the parabolic boundary. We prove a regularity result by finding appropriate spaces for solutions and pre-assigned data in the problem. We use a collection of tools from potential theory, harmonic analysis, and probability. Some lemmas are as important as the main theorem.

Original language | English |
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Pages (from-to) | 1135-1164 |

Number of pages | 30 |

Journal | Journal of Theoretical Probability |

Volume | 26 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2013 Dec 1 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty

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## Cite this

Chang, T., Lee, K., & Yang, M. (2013). On Initial-Boundary Value Problem of the Stochastic Heat Equation in Lipschitz Cylinders.

*Journal of Theoretical Probability*,*26*(4), 1135-1164. https://doi.org/10.1007/s10959-012-0444-1