TY - JOUR
T1 - Maximum likelihood estimation for small noise multiscale diffusions
AU - Spiliopoulos, Konstantinos
AU - Chronopoulou, Alexandra
N1 - Funding Information:
Acknowledgments The authors would like to thank the anonymous reviewer for pointing out a gap in the proof of Theorem 5.1 in the original article, as well as all comments that lead to a significant improvement of the article. K.S. was partially supported, during revisions of this article, by the National Science Foundation (DMS 1312124).
PY - 2013/10
Y1 - 2013/10
N2 - We study the problem of parameter estimation for stochastic differential equations with small noise and fast oscillating parameters. Depending on how fast the intensity of the noise goes to zero relative to the homogenization parameter, we consider three different regimes. For each regime, we construct the maximum likelihood estimator and we study its consistency and asymptotic normality properties. A simulation study for the first order Langevin equation with a two scale potential is also provided.
AB - We study the problem of parameter estimation for stochastic differential equations with small noise and fast oscillating parameters. Depending on how fast the intensity of the noise goes to zero relative to the homogenization parameter, we consider three different regimes. For each regime, we construct the maximum likelihood estimator and we study its consistency and asymptotic normality properties. A simulation study for the first order Langevin equation with a two scale potential is also provided.
KW - Central limit theorem
KW - Dynamical systems
KW - Multiscale diffusions
KW - Parameter estimation
KW - Rough energy landscapes
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U2 - 10.1007/s11203-013-9088-8
DO - 10.1007/s11203-013-9088-8
M3 - Article
AN - SCOPUS:84886773132
VL - 16
SP - 237
EP - 266
JO - Statistical Inference for Stochastic Processes
JF - Statistical Inference for Stochastic Processes
SN - 1387-0874
IS - 3
ER -