Parameter estimation for diffusion process from perturbed discrete observations

We study the parameter estimation for ergodic diffusion process Xt from perturbed observations Y t j = X t j + e t j , j = 1 , … , n where t 1 , … , t n are observation times and the noise e t is a...

[1]  V. Volkonskii,et al.  Some Limit Theorems for Random Functions. II , 1959 .

[2]  Elias Masry,et al.  Multivariate probability density deconvolution for stationary random processes , 1991, IEEE Trans. Inf. Theory.

[3]  R. C. Bradley.  Basic properties of strong mixing conditions. A survey and some open questions , 2005, math/0511078.

[4]  P. Hall,et al.  Martingale Limit Theory and its Application. , 1984 .

[5]  Yacine Aït-Sahalia.  Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed‐form Approximation Approach , 2002 .

[6]  O. Hili,et al.  From Nonparametric Density Estimation to Parametric Estimation of Multidimensional Diffusion Processes , 2015 .

[7]  E. Masry.  Strong consistency and rates for deconvolution of multivariate densities of stationary processes , 1993 .

[8]  N. Yoshida.  Estimation for diffusion processes from discrete observation , 1992 .

[9]  Thierry Jeantheau,et al.  Stochastic volatility models as hidden Markov models and statistical applications , 2000 .

[10]  A. Pedersen.  A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations , 1995 .

[11]  Rafal Kulik.  Nonparametric deconvolution problem for dependent sequences , 2007, 0711.4004.

[12]  R. Beran.  Minimum Hellinger distance estimates for parametric models , 1977 .

[13]  E. Masry.  Asymptotic normality for deconvolution estimators of multivariate densities of stationary processes , 1993 .

[14]  H. Sørensen.  Estimation of diffusion parameters for discretely observed diffusion processes , 2002 .

[15]  Parameter estimation of one-dimensional diffusion process by minimum Hellinger distance method , 2013 .

[16]  Hili Ouagnina,et al.  On the estimation of nonlinear time series models , 1995 .

[17]  M. Rosenblatt.  A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION. , 1956, Proceedings of the National Academy of Sciences of the United States of America.

[18]  A. Meister.  Deconvolution Problems in Nonparametric Statistics , 2009 .