Geodesic
Posterior contraction rate for non-parametric Bayesian estimation of the dispersion coefficient of a stochastic differential equation
Gugushvili, Shota1 ; Spreij, Peter2
1 Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands.
2 Korteweg-de Vries Institute for Mathematics, University of Amsterdam, PO Box 94248, 1090 GE Amsterdam, The Netherlands.
ESAIM: Probability and Statistics, Tome 20 (2016), pp. 143-153

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We consider the problem of non-parametric estimation of the deterministic dispersion coefficient of a linear stochastic differential equation based on discrete time observations on its solution. We take a Bayesian approach to the problem and under suitable regularity assumptions derive the posteror contraction rate. This rate turns out to be the optimal posterior contraction rate.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2016008
Classification : 62G20, 62M05
Keywords: Dispersion coefficient, non-parametric Bayesian estimation, posterior contraction rate, stochastic differential equation

Gugushvili, Shota 1 ; Spreij, Peter 2

1 Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands.
2 Korteweg-de Vries Institute for Mathematics, University of Amsterdam, PO Box 94248, 1090 GE Amsterdam, The Netherlands. 
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     author = {Gugushvili, Shota and Spreij, Peter},
     title = {Posterior contraction rate for non-parametric {Bayesian} estimation of the dispersion coefficient of a stochastic differential equation},
     journal = {ESAIM: Probability and Statistics},
     pages = {143--153},
     publisher = {EDP-Sciences},
     volume = {20},
     year = {2016},
     doi = {10.1051/ps/2016008},
     mrnumber = {3528621},
     zbl = {1357.62200},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2016008/}
}
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Gugushvili, Shota; Spreij, Peter. Posterior contraction rate for non-parametric Bayesian estimation of the dispersion coefficient of a stochastic differential equation. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 143-153. doi: 10.1051/ps/2016008

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