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Martingale solutions and invariant measures for stochastic evolution equations in Banach spaces

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  • Brzezniak, Zdzislaw
  • Gatarek, Dariusz

Abstract

In this paper we study the existence and uniqueness of weak solutions of stochastic differential equations on Banach spaces. We also study the existence of invariant measures for the corresponding Markovian semigroups. Our main tool is the factorization of stochastic convolutions. We close the paper with some examples.

Suggested Citation

  • Brzezniak, Zdzislaw & Gatarek, Dariusz, 1999. "Martingale solutions and invariant measures for stochastic evolution equations in Banach spaces," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 187-225, December.
    • Handle: RePEc:eee:spapps:v:84:y:1999:i:2:p:187-225
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    References listed on IDEAS

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    1. Manthey, Ralf & Maslowski, Bohdan, 1992. "Qualitative behaviour of solutions of stochastic reaction-diffusion equations," Stochastic Processes and their Applications, Elsevier, vol. 43(2), pages 265-289, December.
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    Cited by:

    1. Oleksandr Misiats & Oleksandr Stanzhytskyi & Nung Kwan Yip, 2016. "Existence and Uniqueness of Invariant Measures for Stochastic Reaction–Diffusion Equations in Unbounded Domains," Journal of Theoretical Probability, Springer, vol. 29(3), pages 996-1026, September.
    2. Assing, Sigurd & Manthey, Ralf, 2003. "Invariant measures for stochastic heat equations with unbounded coefficients," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 237-256, February.
    3. Dhariwal, Gaurav & Jüngel, Ansgar & Zamponi, Nicola, 2019. "Global martingale solutions for a stochastic population cross-diffusion system," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3792-3820.
    4. Martin Ondreját & Mark Veraar, 2014. "Weak Characterizations of Stochastic Integrability and Dudley’s Theorem in Infinite Dimensions," Journal of Theoretical Probability, Springer, vol. 27(4), pages 1350-1374, December.
    5. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.

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