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- Title
Central limit theorems for heat equation with time-independent noise: The regular and rough cases.
- Authors
Balan, Raluca M.; Yuan, Wangjun
- Abstract
In this paper, we investigate the asymptotic behavior of the spatial average of the solution to the parabolic Anderson model with time-independent noise in dimension d ≥ 1 , as the domain of the integral becomes large. We consider three cases: (a) the case when the noise has an integrable covariance function; (b) the case when the covariance of the noise is given by the Riesz kernel; (c) the case of the rough noise, i.e. fractional noise with index H ∈ (1 4 , 1 2) in dimension d = 1. In each case, we identify the order of magnitude of the variance of the spatial integral, we prove a quantitative central limit theorem for the normalized spatial integral by estimating its total variation distance to a standard normal distribution, and we give the corresponding functional limit result.
- Subjects
CENTRAL limit theorem; HEAT equation; ANDERSON model; INTEGRAL domains; NOISE; SPATIAL behavior; QUANTUM noise
- Publication
Infinite Dimensional Analysis, Quantum Probability & Related Topics, 2023, Vol 26, Issue 2, p1
- ISSN
0219-0257
- Publication type
Article
- DOI
10.1142/S0219025722500291