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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≥2 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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Cite

BibTeXRIS
BibTeX
@misc{li2026exact,
  title = {{Exact temporal variations and parameter estimation for space--time fractional stochastic heat equations driven by multiplicative noise}},
  author = {Yongkang Li and Yaozhong Hu and Litan Yan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04564},
  eprint = {2610.04564},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04564},
}
RIS
TY  - UNPB
TI  - Exact temporal variations and parameter estimation for space--time fractional stochastic heat equations driven by multiplicative noise
AU  - Yongkang Li
AU  - Yaozhong Hu
AU  - Litan Yan
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04564
UR  - https://arxiv.org/abs/2610.04564
AB  - We establish exact limits for the normalized temporal power variations of every fixed real order γ≥2 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.
ER  -