Non-central limit theorem for the spatial average of the solution to the wave equation with Rosenblatt noise

IF 0.4 Q4 STATISTICS & PROBABILITY Theory of Probability and Mathematical Statistics Pub Date : 2022-05-16 DOI:10.1090/tpms/1167
R. Dhoyer, C. Tudor
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引用次数: 0

Abstract

We analyze the limit behavior in distribution of the spatial average of the solution to the wave equation driven by the two-parameter Rosenblatt process in spatial dimension d = 1 d=1 . We prove that this spatial average satisfies a non-central limit theorem, more precisely it converges in law to a Wiener integral with respect to the Rosenblatt process. We also give a functional version of this limit theorem.
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含Rosenblatt噪声的波动方程解的空间平均的非中心极限定理
本文分析了双参数Rosenblatt过程驱动的波动方程在空间维数d=1时的空间平均解的极限分布行为。我们证明了该空间平均满足一个非中心极限定理,更确切地说,它在定律上收敛于关于Rosenblatt过程的Wiener积分。我们也给出了这个极限定理的泛函形式。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
22
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