For the stochastic differential equation ¶
[math]
¶ the local asymptotic properties of the likelihood function are studied. They depend strongly on the true value of the parameter [math] . Eleven different cases are possible if [math] runs through [math] . Let [math] be the maximum likelihood estimator of [math] based on [math] . Applications to the asymptotic behaviour of [math] as [math] are given.
Publié le : 1999-12-14
Classification:
likelihood function,
limit theorems for martingales,
local asymptotic mixed normality,
local asymptotic normality,
local asymptotic properties,
local asymptotic quadraticity,
maximum likelihood estimator,
stochastic differential equations,
time delay
@article{1143122303,
author = {Gushchin, Alexander A. and K\"uchler, Uwe},
title = {Asymptotic inference for a linear stochastic differential equation with time delay},
journal = {Bernoulli},
volume = {5},
number = {6},
year = {1999},
pages = { 1059-1098},
language = {en},
url = {http://dml.mathdoc.fr/item/1143122303}
}
Gushchin, Alexander A.; Küchler, Uwe. Asymptotic inference for a linear stochastic differential equation with time delay. Bernoulli, Tome 5 (1999) no. 6, pp. 1059-1098. http://gdmltest.u-ga.fr/item/1143122303/