Charles Explorer logo
🇬🇧

SPDEs with Volterra Noise

Publication at Faculty of Mathematics and Physics |
2018

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.