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Stochastic evolution equations with rough boundary noise

Author

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  • Alexandra Neamţu

    (University of Konstanz)

  • Tim Seitz

    (University of Konstanz)

Abstract

We investigate the pathwise well-posedness of stochastic partial differential equations perturbed by multiplicative Neumann boundary noise, such as fractional Brownian motion for $$H\in (1/3,1/2].$$ H ∈ ( 1 / 3 , 1 / 2 ] . Combining functional analytic tools with the controlled rough path approach, we establish global existence of solutions and flows for such equations. For Dirichlet boundary noise we obtain similar results for smoother noise, i.e. in the Young regime.

Suggested Citation

  • Alexandra Neamţu & Tim Seitz, 2023. "Stochastic evolution equations with rough boundary noise," Partial Differential Equations and Applications, Springer, vol. 4(6), pages 1-27, December.
    • Handle: RePEc:spr:pardea:v:4:y:2023:i:6:d:10.1007_s42985-023-00268-6
    DOI: 10.1007/s42985-023-00268-6
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    References listed on IDEAS

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    1. B. Pasik-Duncan & T. E. Duncan & B. Maslowski, 2006. "Linear Stochastic Equations in a Hilbert Space with a Fractional Brownian Motion," International Series in Operations Research & Management Science, in: Houmin Yan & George Yin & Qing Zhang (ed.), Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, chapter 0, pages 201-221, Springer.
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