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Seminar on Probability and Statistics Wednesday November 1 2006 Tokyo 128 3:00-4:10 pm
Some problems related to the estimation of the invariant measure of an ergodic diffusion.
Ilia NEGRI Department of Management and Information Technology, University of Bergamo, Italy Abstract We consider a one dimensional ergodic diffusion process solution of a
stochastic differential equation. We suppose that the diffusion
coefficient is known whereas the drift coefficient $S$ is unknown.
Our interest is the invariant measure of the process denoted as $\mu
$. We denote by $f_S$ and $F_S$ the invariant density and the
invariant distribution function of $\mu$ respectively. We present the
problems of finding efficient estimators when we observe the
trajectory of the diffusion in continuos time over $[0,T]$ and we
study asymptotic properties of the estimators when $T$ goes to infinity.
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