Resumen de On invariant density estimation for ergodic difusion processes

Yury A. Kutoyants

• català

  Presentem una revisi¿o d'alguns resultats sobre estimaci¿o invariant de densitats per observacions de processos de difusi¿o erg`odics, i alguns problemes relacionats. Per a cada problema proposem una cota inferior minimax sobre els riscos de tots els estimadors i aleshores constru¿im un estimador asimpt`oticament eficient. Aquest treball va ser presentat a la Barcelona Conference on Asymptotic Statistics, celebrada a Bellaterra (Barcelona, 2003).

• English

  We present a review of several results concerning invariant density estimation by observations of ergodic diffusion process and some related problems. In every problem we propose a lower minimax bound on the risks of all estimators and then we construct an asymptotically efficient estimator. This contribution has been presented in the Barcelona Conference on Asymptotic Statistics, which took place in Bellaterra (Barcelona, 2003).