In search of necessary and sufficient conditions to solve the parabolic Anderson model with fractional Gaussian noises
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Bibliographic record
Abstract
This paper attempts to obtain necessary and sufficient conditions to solve the parabolic Anderson model with fractional Gaussian noises: ∂ ∂tu(t,x)=1 2Δu(t,x)+u(t,x)W˙(t,x), where W(t,x) is the fractional Brownian field with temporal Hurst parameter H0∈[1∕2,1) and spatial Hurst parameters H =(H1,⋯,Hd) ∈(0,1)d, and W˙(t,x)=∂d+1∂t∂x 1⋯∂xdW(t,x). When d=1 and when (H0,H)∈(1 2,1)×(1 20,1 2) we show that the condition 2H0+H>5∕2 is necessary and sufficient to ensure the existence of a unique solution for the parabolic Anderson Model. When d≥2, we find the necessary and sufficient condition on the Hurst parameters so that each chaos of the solution candidate is square integrable.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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