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.
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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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Čoupek, P., Maslowski, B., Šnupárková, J. (2018). SPDEs with Volterra Noise. In: Eberle, A., Grothaus, M., Hoh, W., Kassmann, M., Stannat, W., Trutnau, G. (eds) Stochastic Partial Differential Equations and Related Fields. SPDERF 2016. Springer Proceedings in Mathematics & Statistics, vol 229. Springer, Cham. https://doi.org/10.1007/978-3-319-74929-7_7
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DOI: https://doi.org/10.1007/978-3-319-74929-7_7
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