Abstract
AbstractIn this paper, we study the central limit theorem for a perturbed stochastic heat equation in the whole space $\mathbb{R}^{d}$Rd, $d\ge 1$d≥1. This equation is driven by a Gaussian noise, which is white in time and correlated in space, and the differential operator is a fractional derivative operator. Burkholder’s inequality plays an important role in the proof.
Funder
Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference13 articles.
1. Boulanba, L., Eddahbi, M., Mellouk, M.: Fractional SPDEs driven by spatially correlated noise: existence of the solution and smoothness of its density. Osaka J. Math. 47, 41–65 (2010)
2. Cheng, L., Li, R., Wang, R., Yao, N.: Moderate deviations for a stochastic wave equation in dimension three. Acta Appl. Math. 158, 67–85 (2018)
3. Da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions. Cambridge University Press, Cambridge (1992)
4. Dalang, R.: Extending the martingale measure stochastic integral with applications to spatially homogeneous s.p.d.e’s. Electron. J. Probab. 4, 6, 1–29 (1999)
5. Dalang, R., Quer-Sardanyons, L.: Stochastic integrals for SPDE’s: a comparison. Expo. Math. 29(1), 67–109 (2011)
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