Small noise asymptotics for linear parabolic SPDEs in two space dimensions with unknown damping factors
Abstract
We study parametric estimation for second order linear parabolic stochastic partial differential equations in two space dimensions with a small volatility parameter driven by a Q-Wiener process with an unknown damping parameter using high frequency spatio-temporal data. We first provide an estimator for the damping parameter of the Q-Wiener process utilizing realized quadratic variations based on spatial and temporal increments. We next propose minimum contrast estimators of the diffusive and advective parameters in the SPDE using a contrast function with the proposed estimator of the damping parameter. We then construct a quasi-maximum likelihood estimator of the reaction parameter in the SPDE using the approximate coordinate process derived from the estimators of the diffusive and advective parameters. We also provide simulation results of the proposed estimators.
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BibTeX
@misc{tonaki2026small,
title = {{Small noise asymptotics for linear parabolic SPDEs in two space dimensions with unknown damping factors}},
author = {Yozo Tonaki and Yusuke Kaino and Masayuki Uchida},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11162},
eprint = {2609.11162},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11162},
}
RIS
TY - UNPB
TI - Small noise asymptotics for linear parabolic SPDEs in two space dimensions with unknown damping factors
AU - Yozo Tonaki
AU - Yusuke Kaino
AU - Masayuki Uchida
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11162
UR - https://arxiv.org/abs/2609.11162
AB - We study parametric estimation for second order linear parabolic stochastic partial differential equations in two space dimensions with a small volatility parameter driven by a Q-Wiener process with an unknown damping parameter using high frequency spatio-temporal data. We first provide an estimator for the damping parameter of the Q-Wiener process utilizing realized quadratic variations based on spatial and temporal increments. We next propose minimum contrast estimators of the diffusive and advective parameters in the SPDE using a contrast function with the proposed estimator of the damping parameter. We then construct a quasi-maximum likelihood estimator of the reaction parameter in the SPDE using the approximate coordinate process derived from the estimators of the diffusive and advective parameters. We also provide simulation results of the proposed estimators.
ER -