乘性噪声驱动的时空分数阶随机热方程的精确时间变化与参数估计
Exact temporal variations and parameter estimation for space--time fractional stochastic heat equations driven by multiplicative noise
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中文总结 AI 辅助
本文针对乘性噪声驱动的时空分数阶随机热方程，建立了任意阶时间幂变差的精确极限，并据此构造了漂移参数和β/α的一致估计量。
中文摘要 AI 辅助
我们为一维时空分数阶随机热方程（由乘性时空白噪声驱动）的温和解建立了每个固定实数阶γ≥2的归一化时间幂变差的精确极限。结果包括精确的归一化二次变差和阶为2α/(α−β)的临界幂变差作为特例。我们还获得了相应的空间平均时间变差。作为应用，我们为漂移参数和比值β/α构造了一致估计量。
英文摘要
We establish exact limits for the normalized temporal power variations of every fixed real order \(γ\geq2\) for the mild solution to a one-dimensional space--time fractional stochastic heat equation driven by multiplicative space--time white noise. The results include the exact normalized quadratic variation and the critical power variation of order \(2α/(α-β)\) as special cases. We also obtain the corresponding spatially averaged temporal variations. As applications, we construct consistent estimators for the drift parameter and for the ratio \(β/α\).
发表机构
- Donghua University（东华大学）
- University of Alberta（阿尔伯塔大学）
机构由 AI 辅助整理，请以论文原文为准。
