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## Asymptotic inference for a linear stochastic differential equation with time delay

Gushchin A. A., Küchler U.

For the stochastic differential equation

$dX\left(t\right)=\left(a X \left( t \right) + b X \left( t - 1 \right)dt+dW\left(t\right),\phantom{\rule{0ex}{0ex}}\right)$

the local asymptotic properties of the likelihood function are studied. They depend strongly on the true value of the parameter