Limit Theorems for Cylindrical Martingale Problems Associated with Lévy Generators

David Criens ()
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David Criens: Technical University of Munich

Journal of Theoretical Probability, 2020, vol. 33, issue 2, 866-905

Abstract: 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; 60J25; 60F05; 60H15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00948-3

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