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Moderate Deviations for Stochastic Heat Equation with Rough Dependence in Space

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Abstract

In this paper, we establish a moderate deviation principle for the stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter H ∈ (1/4, 1/2) in the space variable. The weak convergence approach plays an important role.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Statistics and Mathematics, Nanjing Audit University, Nanjing, 211815, P. R. China

    Jun Feng Liu

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  1. Jun Feng Liu
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Correspondence to Jun Feng Liu.

Additional information

Partially supported by National Natural Science Foundation of China (Grant No. 11771209), Humanities and Social Sciences Foundation of the Ministry of Education of China (Grant No. 18YJCZH101), Natural Science Foundation of Jiangsu Province of China (Grant No. BK20161579), Major Research Plan of Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 18KJA110002), QingLan Project and 333 Talent Training Project of Jiangsu Province (Grant No. BRA2018357)

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Liu, J.F. Moderate Deviations for Stochastic Heat Equation with Rough Dependence in Space. Acta. Math. Sin.-English Ser. 35, 1491–1510 (2019). https://doi.org/10.1007/s10114-019-8149-3

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  • DOI: https://doi.org/10.1007/s10114-019-8149-3

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