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A central limit theorem for the stochastic wave equation with fractional noise. (English. French summary) Zbl 1466.60127

Consider the one-dimensional stochastic heat equation on an interval \([-R,R]\) for \(R>0\) driven by multiplicative fractional Brownian motion with Hurst parameter \(H\in [\frac 1 2, 1]\). Under reasonable conditions the paper proves that when \(R\to\infty\), the normalized spatial average of the solution converges in the total variation distance to a normal distribution, and moreover establishes a fractional central limit theorem.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H07 Stochastic calculus of variations and the Malliavin calculus
60G15 Gaussian processes
60F05 Central limit and other weak theorems
60G22 Fractional processes, including fractional Brownian motion
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References:

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