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

Ruinan Li; Ran Wang

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arXiv · 2609.34066

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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Ruinan Li, Ran Wang. 2026-09-28. Bi-parameter local linearization for the stochastic wave equation with rough noise. https://arxiv.org/abs/2609.34066

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