Work

Local linearization for the nonlinear damped stochastic Klein-Gordon equation

Year: 2026

Type: preprint

Abstract: For the $1+1$ dimensional nonlinear damped stochastic Klein-Gordon equation driven by space-time white noise, we prove that the second-order increments of the solution can be approximated, after scaling with the diffusion coefficient, by those of the corresponding linearized stochastic Klein-Gordon equation. This extends the result of Huang et al. \cite{HOO2024} for the stochastic wave equation. A key difficulty arises from the more complex structure of the Green function, which we overcome by means of subtle analytical estimates. As applications, we analyze the quadratic variation of the solution and construct a consistent estimator for the diffusion parameter.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2601.07176

Authors: Rang, Guanglin, Wang, Ran

Institution: Wuhan University

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: National Science Foundation, National Natural Science Foundation of China

Awards: G4144454573, G6767698131

OpenAlex ID: W7123955406

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