TY - JOUR
T1 - Least squares estimators for stochastic differential equations driven by small Lévy noises
AU - Long, Hongwei
AU - Ma, Chunhua
AU - Shimizu, Yasutaka
N1 - Funding Information:
The authors are grateful to the anonymous referees, the associate editor and the editor for their insightful and valuable comments which have greatly improved the presentation of the paper. The second author was supported by NSFC (Grant Number 11271204). The third author was supported by JSPS KAKENHI (Grant Number 15K05009, 25245033) and JST/CREST.
Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2017/5/1
Y1 - 2017/5/1
N2 - We study parameter estimation for discretely observed stochastic differential equations driven by small Lévy noises. We do not impose Lipschitz condition on the dispersion coefficient function σ and any moment condition on the driving Lévy process, which greatly enhances the applicability of our results to many practical models. Under certain regularity conditions on the drift and dispersion functions, we obtain consistency and rate of convergence of the least squares estimator (LSE) of parameter when ε→0 and n→∞ simultaneously. We present some simulation study on a two-factor financial model driven by stable noises.
AB - We study parameter estimation for discretely observed stochastic differential equations driven by small Lévy noises. We do not impose Lipschitz condition on the dispersion coefficient function σ and any moment condition on the driving Lévy process, which greatly enhances the applicability of our results to many practical models. Under certain regularity conditions on the drift and dispersion functions, we obtain consistency and rate of convergence of the least squares estimator (LSE) of parameter when ε→0 and n→∞ simultaneously. We present some simulation study on a two-factor financial model driven by stable noises.
KW - Asymptotic distribution
KW - Consistency
KW - Discrete observations
KW - Least squares method
KW - Parameter estimation
KW - Stochastic differential equations
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U2 - 10.1016/j.spa.2016.08.006
DO - 10.1016/j.spa.2016.08.006
M3 - Article
AN - SCOPUS:84995471507
SN - 0304-4149
VL - 127
SP - 1475
EP - 1495
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 5
ER -