Maximum likelihood estimation for small noise multiscale diffusions

Konstantinos Spiliopoulos; Alexandra Chronopoulou

doi:10.1007/s11203-013-9088-8

Maximum likelihood estimation for small noise multiscale diffusions

Konstantinos Spiliopoulos
, Alexandra Chronopoulou

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	237-266
Number of pages	30
Journal	Statistical Inference for Stochastic Processes
Volume	16
Issue number	3
DOIs	https://doi.org/10.1007/s11203-013-9088-8
State	Published - Oct 2013
Externally published	Yes

Keywords

Central limit theorem
Dynamical systems
Multiscale diffusions
Parameter estimation
Rough energy landscapes

ASJC Scopus subject areas

Statistics and Probability

Online availability

10.1007/s11203-013-9088-8

Library availability

Discover UIUC Full Text

Cite this

@article{1d26851d541d444aafbe2644266814fc,

title = "Maximum likelihood estimation for small noise multiscale diffusions",

abstract = "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.",

keywords = "Central limit theorem, Dynamical systems, Multiscale diffusions, Parameter estimation, Rough energy landscapes",

author = "Konstantinos Spiliopoulos and Alexandra Chronopoulou",

note = "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).",

year = "2013",

month = oct,

doi = "10.1007/s11203-013-9088-8",

language = "English (US)",

volume = "16",

pages = "237--266",

journal = "Statistical Inference for Stochastic Processes",

issn = "1387-0874",

publisher = "Springer Science and Business Media B.V.",

number = "3",

}

TY - JOUR

T1 - Maximum likelihood estimation for small noise multiscale diffusions

AU - Spiliopoulos, Konstantinos

AU - Chronopoulou, Alexandra

N1 - 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

UR - https://www.scopus.com/pages/publications/84886773132

UR - https://www.scopus.com/pages/publications/84886773132#tab=citedBy

U2 - 10.1007/s11203-013-9088-8

DO - 10.1007/s11203-013-9088-8

M3 - Article

AN - SCOPUS:84886773132

SN - 1387-0874

VL - 16

SP - 237

EP - 266

JO - Statistical Inference for Stochastic Processes

JF - Statistical Inference for Stochastic Processes

IS - 3

ER -

Maximum likelihood estimation for small noise multiscale diffusions

Abstract

Keywords

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this