JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (6): 17-22.doi: 10.6040/j.issn.1671-9352.0.2019.026

Previous Articles    

Hypothesis testing of maximum likelihood estimation for stochastic PDE

WANG Xiao-wen, LYU Yan*   

  1. School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China
  • Published:2020-06-01

PDF (PC)

784

Abstract: The hypothesis testing problem for the parameter estimation for a class of stochastic partial differential equation driven by additive noise is studied. The explicit expressions for rejection domain of the unknown parameter in two asymptotic cases: T→∞ with N fixed and N→∞ with T fixed are shown and their asymptotic properties are further proved.

Key words: hypothetical test, stochastic partial differential equations, rejection region

CLC Number: 

  • O211.63
[1] CIALENCO I, XU L. Hypothesis testing for stochastic PDEs driven by additive noise[J]. Stochastic Processes and their Applications, 2015, 125(3):819-866.
[2] CIALENCO I, XU L. A note on error estimation for hypothesis testing problems for some linear SPDEs[J]. Stoch Partial Differ Equ Anal Comput, 2014, 2(3):408-431.
[3] LOTOTSKY S V. Statistical inference for stochastic parabolic equations: a spectral approach[J]. Publ Mat, 2009, 53(1):3-45.
[4] MARKUSSEN B. Likelihood inference for a discretely observed stochastic partial differential equation[J]. Bernoulli, 2003, 9(5):745-762.
[5] TEMAM R. Infinite-dimensional dynamical systems in mechanics and physics[M]. New York: Springer-Verlag, 1997.
[6] 厄克森达尔.随机微分方程导论与应用[M]. 刘金山,吴付科,译.北京:科学出版社, 2012. ØKSENDAL B. Introduction and application of stochastic differential equations[M]. Beijing: Science Press, 2012.
[7] HUEBNER M, ROZOVSKII B L. On asymptotic properties of maximum likelihood estimators for parabolic stochastics PDEs[J]. Probability Theory and Related Fields, 1995, 103(2):143-163.
[8] JANÁK J. Parameter estimation for stochastic partial differential equations of second order[J]. Applied Mathematics & Optimization, 2018: 1-45.
[9] ROUGEMONT J. Space-time invariant measures, entropy, and dimension for stochastic Ginzburg-Landau equations[J]. Communications in Mathematical Physics, 2002, 225:423-448.
[10] CIALENCO I, LOTOTSKY S V. Parameter estimation in diagonalizable bilinear stochastic parabolic equations[J]. Stat Inference Stoch Process, 2009, 12(3):203-219.
[11] 吴向阳. 一类非线性随机偏微分方程参数的假设检验[D]. 南京: 南京大学, 2018. WU Xiangyang. Hypothesis testing for the parameters of a class of nonlinear stochastic partial differential equations[D]. Nanjing: Nanjing University, 2018.
[1] LI Yuan-fei. Continuous dependence on viscosity coefficient for primitive equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 12-23.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd