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Cylindrical Martingale Problems Associated with Lévy Generators

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  • David Criens

    (Technical University of Munich)

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.

Suggested Citation

  • David Criens, 2019. "Cylindrical Martingale Problems Associated with Lévy Generators," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1306-1359, September.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:3:d:10.1007_s10959-018-0814-4
    DOI: 10.1007/s10959-018-0814-4
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    References listed on IDEAS

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    1. Goldys, Benjamin & Röckner, Michael & Zhang, Xicheng, 2009. "Martingale solutions and Markov selections for stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1725-1764, May.
    2. G. Prato & F. Flandoli & E. Priola & M. Röckner, 2015. "Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1571-1600, December.
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    Cited by:

    1. David Criens, 2020. "Correction to: Cylindrical Martingale Problems Associated with Lévy Generators," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1791-1800, September.
    2. David Criens, 2020. "Limit Theorems for Cylindrical Martingale Problems Associated with Lévy Generators," Journal of Theoretical Probability, Springer, vol. 33(2), pages 866-905, June.

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