Cylindrical Martingale Problems Associated with Lévy Generators

David Criens ()
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David Criens: Technical University of Munich

Journal of Theoretical Probability, 2019, vol. 32, issue 3, 1306-1359

Abstract: Abstract We introduce and discuss Lévy-type cylindrical martingale problems on separable reflexive Banach spaces. Our main observations are the following: Cylindrical martingale problems have a one-to-one relation to weak solutions of stochastic partial differential equations, and well-posed problems possess the strong Markov property and a Cameron–Martin–Girsanov-type formula holds. As applications, we derive existence and uniqueness results.

Keywords: Cylindrical martingale problem; Lévy generator; Markov property; Cameron–Martin–Girsanov formula; Stochastic partial differential equation; 60J25; 60H15; 60G48 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0814-4

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