Local linearization for estimating the diffusion parameter of nonlinear stochastic wave equations with spatially correlated noise

We study the bi-parameter local linearization of the one-dimensional nonlinear stochastic wave equation driven by Gaussian noise, which is white in time and processes a spatially homogeneous covariance structure of Riesz-kernel type. Specifically, we establish that the second-order increments of the solution can be approximated by those of the corresponding linearized wave equation, modulated by the diffusion coefficient. This result extends the previous work of Huang et al. \cite{HOO2024}, which considered the case of space-time white noise. As applications, we analyze the quadratic variation of the solution and construct a consistent estimator for the diffusion parameter. MSC: 60H15; 60G17; 60G22.