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PreprintCC BY 4.0arXiv

Bi-parameter local linearization for the stochastic wave equation with rough noise

  • Ruinan Li
  • Ran Wang
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Abstract

We study a one-dimensional nonlinear stochastic wave equation driven by Gaussian noise that is white in time and rough in space. We prove a bi-parameter local linearization for mixed increments along the two characteristic directions. The proof combines characteristic cancellation with a localized fractional-energy estimate that controls boundary interactions caused by the rough spatial noise. As an application, we establish quadratic-variation limits on arbitrary anisotropic rectangular meshes and construct a consistent estimator of a multiplicative diffusion parameter. Numerical experiments illustrate the finite-sample performance of the estimator.

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Cite

BibTeXRIS
BibTeX
@misc{li2026biparameter,
  title = {{Bi-parameter local linearization for the stochastic wave equation with rough noise}},
  author = {Ruinan Li and Ran Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34066},
  eprint = {2609.34066},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34066},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Bi-parameter local linearization for the stochastic wave equation with rough noise
AU  - Ruinan Li
AU  - Ran Wang
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34066
UR  - https://arxiv.org/abs/2609.34066
AB  - We study a one-dimensional nonlinear stochastic wave equation driven by Gaussian noise that is white in time and rough in space. We prove a bi-parameter local linearization for mixed increments along the two characteristic directions. The proof combines characteristic cancellation with a localized fractional-energy estimate that controls boundary interactions caused by the rough spatial noise. As an application, we establish quadratic-variation limits on arbitrary anisotropic rectangular meshes and construct a consistent estimator of a multiplicative diffusion parameter. Numerical experiments illustrate the finite-sample performance of the estimator.
ER  -