TY - JOUR
T1 - Estimation of parameters for discretely observed diffusion processes with a variety of rates for information
AU - Shimizu, Yasutaka
N1 - Funding Information:
Acknowledgments The author expresses many thanks to anonymous referees for their helpful comments and instructions. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists (B), 2009, no. 21740073, and JST, CREST.
PY - 2012/6
Y1 - 2012/6
N2 - A specific form of stochastic differential equation with unknown parameters are considered. We do not necessarily assume ergodicity or recurrency, and any moment conditions for the true process, but some tightness conditions for an information-like quantity. The interest is to estimate the parameters from discrete observations the step size of which tends to zero. Consistency and the rate of convergence of proposed estimators are presented. The rate is deduced naturally from the rate for the information-like quantities.
AB - A specific form of stochastic differential equation with unknown parameters are considered. We do not necessarily assume ergodicity or recurrency, and any moment conditions for the true process, but some tightness conditions for an information-like quantity. The interest is to estimate the parameters from discrete observations the step size of which tends to zero. Consistency and the rate of convergence of proposed estimators are presented. The rate is deduced naturally from the rate for the information-like quantities.
KW - Consistency
KW - Discrete observations
KW - Non-ergodic diffusions
KW - Normalized information
KW - Parametric inference
KW - Rates of convergence
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U2 - 10.1007/s10463-010-0323-4
DO - 10.1007/s10463-010-0323-4
M3 - Article
AN - SCOPUS:84856606443
SN - 0020-3157
VL - 64
SP - 545
EP - 575
JO - Annals of the Institute of Statistical Mathematics
JF - Annals of the Institute of Statistical Mathematics
IS - 3
ER -