Trajectory fitting estimators for SPDEs driven by additive noise

Igor Cialenco (), Ruoting Gong () and Yicong Huang ()
Additional contact information
Igor Cialenco: Illinois Institute of Technology
Ruoting Gong: Illinois Institute of Technology
Yicong Huang: Illinois Institute of Technology

Statistical Inference for Stochastic Processes, 2018, vol. 21, issue 1, No 1, 19 pages

Abstract: Abstract In this paper we study the problem of estimating the drift/viscosity coefficient for a large class of linear, parabolic stochastic partial differential equations (SPDEs) driven by an additive space-time noise. We propose a new class of estimators, called trajectory fitting estimators (TFEs). The estimators are constructed by fitting the observed trajectory with an artificial one, and can be viewed as an analog to the classical least squares estimators from the time-series analysis. As in the existing literature on statistical inference for SPDEs, we take a spectral approach, and assume that we observe the first N Fourier modes of the solution, and we study the consistency and the asymptotic normality of the TFE, as $$N\rightarrow \infty $$ N → ∞ .

Keywords: Stochastic partial differential equations; Trajectory fitting estimator; Parameter estimation; Inverse problems; Estimation of viscosity coefficient; 60H15; 35Q30; 65L09 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s11203-016-9152-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sistpr:v:21:y:2018:i:1:d:10.1007_s11203-016-9152-2

Ordering information: This journal article can be ordered from
http://www.springer. ... ty/journal/11203/PS2

DOI: 10.1007/s11203-016-9152-2

Access Statistics for this article

Statistical Inference for Stochastic Processes is currently edited by Denis Bosq, Yury A. Kutoyants and Marc Hallin

More articles in Statistical Inference for Stochastic Processes from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().