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Stability Properties of Mild Solutions of SPDEs Related to Pseudo Differential Equations

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Quantum and Stochastic Mathematical Physics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 377))

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Abstract

This is a review article which presents part of the contribution of Sergio Albeverio to the study of existence and uniqueness of solutions of SPDEs driven by jump processes and their stability properties. The results on stability properties obtained in Albeverio et al. (Random Oper. Stoch. Equ. 25(2):79–105, 2017 [4]) are presented in a slightly simplified and different way.

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Acknowledgements

I thank Peter Kuchling and Baris Ugurcan for a careful reading of part of this article.

Comment by Barbara Rüdiger My co-author and friend V. Mandrekar (Atma) passed away the 23 June 2021. A couple of days before his departure he contacted me through email to make sure the procedure for the submission of this article would be successful. The invitation to contribute to this Volume, dedicated to Sergio Albeverio, was accepted by him with enthusiasm.

Atma and Sergio had, to my feeling, a deep respect for each other and, despite the geographic distance, a solid friendship. I think that this friendship and respect is also due to common aspects they have in their character and soul: both are very generous in sharing with other scientists their original ideas. Both trust in youngsters and enjoy knowing that they can contribute to these with their own developments and ideas, as well. This way they both are friends, supporters, coaches and co-authors to many young (and in the meanwhile older) mathematicians and physists. I feel very lucky to be among them.

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Authors and Affiliations

  1. Department of Statistics and Probability, Michigan State University, East Lansing, MI, USA

    V. Mandrekar

  2. Bergische Universität Wuppertal, Gaußstrasse 20, 42119, Wuppertal, Germany

    B. Rüdiger

Authors
  1. V. Mandrekar
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  2. B. Rüdiger
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Corresponding author

Correspondence to B. Rüdiger .

Editor information

Editors and Affiliations

  1. Faculty of Technology, Linnaeus University, Växjo, Sweden

    Astrid Hilbert

  2. Department of Economics, Insubria University, Varese, Italy

    Elisa Mastrogiacomo

  3. Department of Mathematics, University of Trento, Povo, Trento, Italy

    Sonia Mazzucchi

  4. Applied Mathematics / Stochastic, University of Wuppertal, Wuppertal, Germany

    Barbara Rüdiger

  5. Department of Mathematics, University of MIlan, Milano, Italy

    Stefania Ugolini

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Mandrekar, V., Rüdiger, B. (2023). Stability Properties of Mild Solutions of SPDEs Related to Pseudo Differential Equations. In: Hilbert, A., Mastrogiacomo, E., Mazzucchi, S., Rüdiger, B., Ugolini, S. (eds) Quantum and Stochastic Mathematical Physics. Springer Proceedings in Mathematics & Statistics, vol 377. Springer, Cham. https://doi.org/10.1007/978-3-031-14031-0_13

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