Quadratic variation and drift parameter estimation for the stochastic wave equation with space-time white noise

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Stochastics and Dynamics Pub Date : 2022-04-29 DOI:10.1142/s0219493722400147

Obayda Assaad, Julie Gamain, C. Tudor

引用次数: 1

Abstract

We study the quadratic variations (in time and in space) of the solution to the stochastic wave equation driven by the space-time white noise. We give their limit (almost surely and in [Formula: see text]) and we prove that these variations satisfy, after a proper renormalization, a Central Limit Theorem. We apply the quadratic variation to define and analyze estimators for the drift parameter of the wave equation.

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时空白噪声随机波动方程的二次变分及漂移参数估计

我们研究了由时空白噪声驱动的随机波动方程解的二次变化（在时间和空间上）。我们给出了它们的极限（几乎可以肯定，并且在[公式：见正文]中），并且我们证明了在适当的重整化之后，这些变化满足中心极限定理。我们应用二次变分来定义和分析波动方程漂移参数的估计量。

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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来源期刊

Stochastics and Dynamics 数学-统计学与概率论

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal is devoted to publishing high quality papers in modeling, analyzing, quantifying and predicting stochastic phenomena in science and engineering from a dynamical system''s point of view. Papers can be about theory, experiments, algorithms, numerical simulation and applications. Papers studying the dynamics of stochastic phenomena by means of random or stochastic ordinary, partial or functional differential equations or random mappings are particularly welcome, and so are studies of stochasticity in deterministic systems.