Skip to content
DraconiticResearch
Search Sources API
194,220 studies31 sourcesUpdated 27 min ago
PreprintCC BY 4.0arXiv

Gaussian fluctuations for the stochastic wave equation with drift

  • Raluca M. Balan
  • William D. Stephenson
Open at sourcePDFDOICite

Abstract

In this article, we study the spatial fluctuations of the solution to the stochastic wave equation with a nonlinear drift and multiplicative Gaussian noise in dimensions one and two. The noise is white in time, and its spatial covariance is either integrable or given by a Riesz kernel; space-time white noise in dimension one is also included. We establish spatial ergodicity, convergence of the rescaled covariance, and prove a quantitative central limit theorem for the spatial fluctuations. We also obtain the corresponding functional central limit theorem. Our approach exploits the compact support of the wave kernel to obtain an estimate for the spatially integrated second Malliavin derivative which is compatible with a bound for the total variation. Further arguments based on the Clark-Ocone formula are used to control the drift contributions.

Related

  1. Drift Estimation for a Multi-Dimensional Lévy-Driven Stochastic Differential Equation Using Deep Neural Networks
    Taisei Noguchi, Teppei Ogihara
    arXivPreprintarXiv licenceFull textProbabilityStatisticsarXiv
  2. Stochastic damped wave and Euler-Bernoulli equations with singular locally Hölder continuous drift
    Davide Addona, Davide Augusto Bignamini
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsProbabilityarXiv
  3. Central limit theorems for stochastic heat equation driven by Gaussian noise with heat-kernel covariance
    Meng Wang, Wangjun Yuan
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  4. Finite-time transition to intermittency for a stochastic heat equation driven by the square of a Gaussian field
    Philippe Mounaix
    Journal of Physics A: Mathematical and TheoreticalPeer-reviewedCC BY 4.0Full textMathematical physicsHAL
  5. Bi-parameter local linearization for the stochastic wave equation with rough noise
    Ruinan Li, Ran Wang
    arXivPreprintCC BY 4.0Full textProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{balan2026gaussian,
  title = {{Gaussian fluctuations for the stochastic wave equation with drift}},
  author = {Raluca M. Balan and William D. Stephenson},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.21258},
  eprint = {2609.21258},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21258},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Gaussian fluctuations for the stochastic wave equation with drift
AU  - Raluca M. Balan
AU  - William D. Stephenson
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.21258
UR  - https://arxiv.org/abs/2609.21258
AB  - In this article, we study the spatial fluctuations of the solution to the stochastic wave equation with a nonlinear drift and multiplicative Gaussian noise in dimensions one and two. The noise is white in time, and its spatial covariance is either integrable or given by a Riesz kernel; space-time white noise in dimension one is also included. We establish spatial ergodicity, convergence of the rescaled covariance, and prove a quantitative central limit theorem for the spatial fluctuations. We also obtain the corresponding functional central limit theorem. Our approach exploits the compact support of the wave kernel to obtain an estimate for the spatially integrated second Malliavin derivative which is compatible with a bound for the total variation. Further arguments based on the Clark-Ocone formula are used to control the drift contributions.
ER  -