A Central Limit Theorem for Stochastic Heat Equations in Random Environment

Lu Xu ()
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Lu Xu: The University of Tokyo

Journal of Theoretical Probability, 2018, vol. 31, issue 3, 1356-1379

Abstract: Abstract In this article, we investigate the asymptotic behavior of the solution to a one-dimensional stochastic heat equation with random nonlinear term generated by a stationary, ergodic random field. We extend the well-known central limit theorem for finite-dimensional diffusions in random environment to this infinite-dimensional setting. Due to our result, a central limit theorem in $$L^1$$ L 1 sense with respect to the randomness of the environment holds under a diffusive time scaling. The limit distribution is a centered Gaussian law whose covariance operator is explicitly described. The distribution concentrates only on the space of constant functions.

Keywords: Stochastic heat equation; Random environment; Central limit theorem; 60F05; 60H15; 60K37 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-017-0748-2

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