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• W3106915005 abstract "In light of recent work on particles fluctuating in linear viscoelastic fluids, we study a linear stochastic partial-integro-differential equation with memory that is driven by a stationary noise on a bounded, smooth domain. Using the framework of generalized stationary solutions introduced in~cite{mckinley2018anomalous}, we provide sufficient conditions on the differential operator and the noise to obtain the existence as well as Holder regularity of the stationary solutions for the concerned equation. As an application of the regularity results, we compare to analogous classical results for the stochastic heat equation. When the 1d stochastic heat equation is driven by white noise, solutions are continuous with space and time regularity that is Holder $(1/2-ep)$ and $(1/4-ep)$ respectively. When driven by colored-in-space noise, solutions can have a range of regularity properties depending on the structure of the noise. Here, we show that the particular form of colored-in-time memory that arises in viscoelastic diffusion applications, satisfying what is called the Fluctuation--Dissipation relationship, yields sample paths that are Holder $(1/2-ep)$ and $(1/2-ep)$ in space and time." @default.
• W3106915005 created "2020-12-07" @default.
• W3106915005 creator A5059131872 @default.
• W3106915005 creator A5090274747 @default.
• W3106915005 date "2020-11-19" @default.
• W3106915005 modified "2023-09-27" @default.
• W3106915005 title "On the Holder regularity of a linear stochastic partial-integro-differential equation with memory" @default.
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• W3106915005 hasPublicationYear "2020" @default.
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