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SPDEs with Volterra Noise

  • Petr Čoupek
  • Bohdan MaslowskiEmail author
  • Jana Šnupárková
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 229)

Abstract

Recent results on linear stochastic partial differential equations driven by Volterra processes with linear or bilinear noise are briefly reviewed and partially extended. In the linear case, existence and regularity properties of stochastic convolution integral are established and the results are applied to 1D linear parabolic PDEs with boundary noise of Volterra type. For the equations with bilinear noise, existence and large time behaviour of solutions are studied.

Keywords

Volterra process Rosenblatt process Stochastic evolution equation Additive noise Bilinear noise 

2010 Mathematics Subject Classification

60H15 60G22 

Notes

Acknowledgements

The authors are grateful to the anonymous referee for their valuable suggestions. The first author was supported by the Charles University grant GAUK No. 322715 and SVV 2016 No. 260334. The second author was supported by the Czech Science Foundation grant GAČR No. 15-08819S.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Petr Čoupek
    • 1
  • Bohdan Maslowski
    • 1
    Email author
  • Jana Šnupárková
    • 2
  1. 1.Faculty of Mathematics and PhysicsCharles UniversityPraha 8Czech Republic
  2. 2.Faculty of Chemical EngineeringUniversity of Chemistry and Technology PraguePraha 6Czech Republic

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