ASYMPTOTIC PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR FOR STOCHASTIC PARABOLIC EQUATIONS WITH ADDITIVE FRACTIONAL BROWNIAN MOTION-Reference-Cited by-同舟云学术

ASYMPTOTIC PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR FOR STOCHASTIC PARABOLIC EQUATIONS WITH ADDITIVE FRACTIONAL BROWNIAN MOTION

Published:2009-06 Issue:02 Volume:09 Page:169-185
ISSN:0219-4937
Container-title:Stochastics and Dynamics
language:en
Short-container-title:Stoch. Dyn.

Author:

CIALENCO IGOR¹,LOTOTSKY SERGEY V.²,POSPÍŠIL JAN³

Affiliation:

1. Department of Applied Mathematics, Illinois Institute of Technology, 10 West 32nd Str, Bld E1, Room 208, Chicago, IL 60616, USA

2. Department of Mathematics, University of Southern California, 3620 S. Vermont Avenue, KAP 108, Los Angeles, CA 90089, USA

3. Department of Mathematics, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech Republic

Abstract

A parameter estimation problem is considered for a diagonalizable stochastic evolution equation using a finite number of the Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and fractional in time with the Hurst parameter H ≥ 1/2. The objective is to study asymptotic properties of the maximum likelihood estimator as the number of the Fourier coefficients increases. A necessary and sufficient condition for consistency and asymptotic normality is presented in terms of the eigenvalues of the operators in the equation.

Publisher

World Scientific Pub Co Pte Lt

Subject

Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219493709002610

Reference18 articles.

1. M. Huebner, R. Khasminskii and B. L. Rozovskii, Stochastic Processes: A Volume in Honor of G. Kallianpur, eds. S. Cambanis (Springer, 1992) pp. 149–160.

2. On asymptotic properties of maximum likelihood estimators for parabolic stochastic PDE's

3. Statistical Estimation

4. Spectral Theory of Differential Operators

Cited by 58 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Research on privacy information retrieval model based on hybrid homomorphic encryption;Cybersecurity;2023-12-01

2. The CKKS FHE Scheme;Synthesis Lectures on Computer Architecture;2023

3. Introduction;Synthesis Lectures on Computer Architecture;2023

4. Summary;Synthesis Lectures on Computer Architecture;2023

5. Parameter-dependent filtering of Gaussian processes in Hilbert spaces;Stochastic Analysis and Applications;2022-05-29