含Rosenblatt噪声的波动方程解的空间平均的非中心极限定理

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

摘要

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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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来源期刊

Theory of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

CiteScore

1.30

自引率

0.00%

发文量