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arXiv · 2610.04564

Exact temporal variations and parameter estimation for space--time fractional stochastic heat equations driven by multiplicative noise

Yongkang Li·Yaozhong Hu·Litan Yan
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Abstract

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 \(β/α\).

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Yongkang Li, Yaozhong Hu, Litan Yan. 2026-10-03. Exact temporal variations and parameter estimation for space--time fractional stochastic heat equations driven by multiplicative noise. https://arxiv.org/abs/2610.04564

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