Large deviations for stochastic heat equations with memory driven by Lévy-type noise

Markus Riedle; Jianliang Zhai

doi:10.3934/dcds.2018080

Article Contents

2018, Volume 38, Issue 4: 1983-2005. Doi: 10.3934/dcds.2018080

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Large deviations for stochastic heat equations with memory driven by Lévy-type noise

Markus Riedle^1, and
Jianliang Zhai^2, ,

1.
Department of Mathematics, King's College London, London WC2R 2LS, United Kingdom
2.
School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China

* Corresponding author
* Corresponding author

Received: January 2017

Revised: October 2017

Published: July 2018

The second author acknowledges funding by K. C. Wong Foundation for a 1-year fellowship at King's College London.

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Abstract

For a heat equation with memory driven by a Lévy-type noise we establish the existence of a unique solution. The main part of the article focuses on the Freidlin-Wentzell large deviation principle of the solutions of heat equation with memory driven by a Lévy-type noise. For this purpose, we exploit the recently introduced weak convergence approach.

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Mathematics Subject Classification: Primary: 60H15, 60F10; Secondary: 37L55.

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References

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