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Limit Theorems for Cylindrical Martingale Problems Associated with Lévy Generators

  • David CriensEmail author
Article
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Abstract

We prove limit theorems for cylindrical martingale problems associated with Lévy generators. Furthermore, we give sufficient and necessary conditions for the Feller property of well-posed problems with continuous coefficients. We discuss two applications. First, we derive continuity and linear growth conditions for the existence of weak solutions to infinite-dimensional stochastic differential equations driven by Lévy noise. Second, we derive continuity, local boundedness and linear growth conditions for limit theorems and the Feller property of weak solutions to stochastic partial differential equations driven by Wiener noise.

Keywords

Cylindrical martingale problem Lévy generator Limit theorem Feller process Stochastic partial differential equation Jump-diffusion existence theorem 

Mathematics Subject Classification (2010)

60J25 60F05 60H15 

Notes

Acknowledgements

The author is grateful to the anonymous referees for many helpful comments.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Center for MathematicsTechnical University of MunichMunichGermany

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