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- Publisher
- Springer Journals
- Copyright
- Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-018-9506-9
- Publisher site
- See Article on Publisher Site
Abstract
Stochastic partial differential equations of second order with two unknown parameters are studied. Based on ergodicity, two suitable families of minimum contrast estimators are introduced. Strong consistency and asymptotic normality of estimators are proved. The results are applied to hyperbolic equations perturbed by Brownian noise. Keywords Parameter estimation · Strong consistency · Asymptotic normality Mathematics Subject Classification 62M05 · 93E10 · 60G35 · 60H15 1 Introduction Statistical inference for stochastic partial differential equations driven by standard Brownian motion has been recently extensively studied. While many authors use max- imum likelihood estimators (MLE) as the most frequent tool (for example [9], where the parameter is linearly built in the drift, or [1] for the case of discrete observations), we are interested in minimum contrast estimator (MCE), which has been studied since 1980s (see [4] and [5]). In more recent works, the (MCE) has also been provided for the SPDEs driven by fractional Brownian motion (for example [8]or[7]). In this work, we study parameter estimation for SPDEs of second order, in particular, for the following wave equation with strong damping This paper has been produced with contribution of long term institutional support of research activities by Faculty of Informatics and Statistics,
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Jul 13, 2018