Kavli Affiliate: Ran Wang
| First 5 Authors: Guoping Liu, Guoping Liu, , ,
| Summary:
We study the bi-parameter local linearization of the one-dimensional
nonlinear stochastic wave equation driven by a Gaussian noise, which is white
in time and has a spatially homogeneous covariance structure of Riesz-kernel
type. 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. These findings extend the previous results of
Huang et al. citeHOO2024, which addressed 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.
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