Trajectory fitting estimators for SPDEs driven by additive noise
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 est...
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| Veröffentlicht in: | Statistical inference for stochastic processes : an international journal devoted to time series analysis and the statistics of continuous time processes and dynamic systems 2018-04, Vol.21 (1), p.1-19 |
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| container_title | Statistical inference for stochastic processes : an international journal devoted to time series analysis and the statistics of continuous time processes and dynamic systems |
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| creator | Cialenco, Igor Gong, Ruoting Huang, Yicong |
| description | 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
→
∞
. |
| doi_str_mv | 10.1007/s11203-016-9152-2 |
| format | Article |
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N
Fourier modes of the solution, and we study the consistency and the asymptotic normality of the TFE, as
N
→
∞
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N
Fourier modes of the solution, and we study the consistency and the asymptotic normality of the TFE, as
N
→
∞
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N
Fourier modes of the solution, and we study the consistency and the asymptotic normality of the TFE, as
N
→
∞
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| ispartof | Statistical inference for stochastic processes : an international journal devoted to time series analysis and the statistics of continuous time processes and dynamic systems, 2018-04, Vol.21 (1), p.1-19 |
| issn | 1387-0874 1572-9311 |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Economic models Estimating techniques Estimators Mathematics Mathematics and Statistics Normality Partial differential equations Probability Theory and Stochastic Processes Regression analysis Statistical inference Statistical Theory and Methods Time series Trajectory analysis |
| title | Trajectory fitting estimators for SPDEs driven by additive noise |
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