Central limit theorem for the solution to the heat equation with moving time

Liu Junfeng; Tudor Ciprian A.

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Central limit theorem for the solution to the heat equation with moving time

机译：带移动时间的热方程解的中心极限定理

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摘要

We consider the solution to the stochastic heat equation driven by the time-space white noise and study the asymptotic behavior of its spatial quadratic variations with "moving time", meaning that the time variable is not fixed and its values are allowed to be very big or very small. We investigate the limit distribution of these variations via Malliavin calculus.

机译：我们考虑由时空白噪声驱动的随机热方程的解，并研究其空间二次变化随“移动时间”的渐近行为，这意味着时间变量不是固定的，并且其值可以很大或很小。我们通过Malliavin微积分研究了这些变异的极限分布。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2016年第1期|共17页
作者
Liu Junfeng; Tudor Ciprian A.;
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正文语种 eng
中图分类物理学;
关键词
Stochastic heat equation; Malliavin calculus; multiple Wiener-Ito integrals; asymptotic normality; Stein method;

机译：随机热方程;Malliavin演算;多个Wiener-Ito积分;渐近正态性;Stein方法;

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专利

1. Central limit theorem for the solution to the heat equation with moving time [J] . Liu Junfeng, Tudor Ciprian A. Infinite dimensional analysis, quantum probability, and related topics . 2016,第1期

机译：带移动时间的热方程解的中心极限定理
2. Central limit theorems for solutions of the Kac equation: speed of approach to equilibrium in weak metrics [J] . Ester Gabetta, Eugenio Regazzini Probability Theory and Related Fields . 2010,第3a4期

机译：Kac方程解的中心极限定理：弱度量中接近平衡的速度
3. A Central Limit Theorem for Stochastic Heat Equations in Random Environment [J] . Xu Lu Journal of theoretical probability . 2018,第3期

机译：随机环境中随机热方程的中央极限定理
4. Fundamental Solutions to the Central Symmetric Space-Time Fractional Heat Conduction Equation and Associated Thermal Stresses [C] . Yuriy Povstenko Conference on non-integer order calculus and its applications . 2013

机译：中心对称时空分数热传导方程和相关热应力的基本解
5. LIMIT THEOREMS FOR INFINITE URN MODELS IN PROBABILITY THEORY (PARTICLES, CENTRAL LIMIT, CELLS). [D] . DUTKO, MICHAEL. 1984

机译：概率理论中无穷大模型的极限定理（粒子，中心极限，单元）。
6. Nonparametric Functional Central Limit Theorem for Time Series Regression with Application to Self-normalized Confidence Interval [O] . Seonjin Kim, Zhibiao Zhao, Xiaofeng Shao -1

机译：时间序列回归的非参数泛函中心极限定理及其在自标准化置信区间中的应用
7. A central limit theorem for stochastic heat equations in random environment [O] . Xu, Lu 2017

机译：随机热随机方程的中心极限定理环境
8. Polling Systems: Moment Stability of Station Times and Central Limit Theorems [R] . Altman, E., Spieksma, F. 1992

机译：轮询系统：台站时间和中心极限定理的矩稳定性

Central limit theorem for the solution to the heat equation with moving time

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