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- W4308494175 abstract "This paper provides necessary as well as sufficient conditions on the Hurst parameters so that the continuous time parabolic Anderson model $$frac{partial u}{partial t}=frac{1}{2}Delta +u{dot{W}}$$ on $$[0, infty )times {{mathbb {R}}}^d $$ with $$dge 1$$ has a unique random field solution, where W(t, x) is a fractional Brownian sheet on $$[0, infty )times {{mathbb {R}}}^d$$ and formally $$dot{W} =frac{partial ^{d+1}}{partial t partial x_1 cdots partial x_d} W(t, x)$$ . When the noise W(t, x) is white in time, our condition is both necessary and sufficient when the initial data u(0, x) is bounded between two positive constants. When the noise is fractional in time with Hurst parameter $$H_0>1/2$$ , our sufficient condition, which improves the known results in the literature, is different from the necessary one." @default.
- W4308494175 created "2022-11-12" @default.
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- W4308494175 date "2022-11-03" @default.
- W4308494175 modified "2023-10-14" @default.
- W4308494175 title "Solvability of Parabolic Anderson Equation with Fractional Gaussian Noise" @default.
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- W4308494175 doi "https://doi.org/10.1007/s40304-021-00264-5" @default.
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