Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Li, Ruinan, Wang, Ran
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7214713098