Nonparametric Statistics for Diffusion Processes : The multidimensional case

Annamaria Bianchi

ISBN 10: 3838317459 / ISBN 13: 9783838317458

Verlag: LAP LAMBERT Academic Publishing, 2009

Beschreibung

nach der Bestellung gedruckt Neuware - Printed after ordering - Diffusion processes are widely used in many applied disciplines, such as biology, physics and financial mathematics. From the applied perspective multivariate diffusions are more interesting than scalar ones since only multidimensional models can describe the evolution of variables which interact among themselves. It is therefore very important to be able to identify such models starting from the observed data. However, while the scalar case has been widely studied, there are very few results for the multidimensional problem since these models present greater difficulties. This work provides a first insight into the problem of identification of multidimensional diffusions: the purpose is to estimate density and drift by the observation of a trajectory of a d-dimensional homogeneous diffusion process with a unique invariant density. Estimators of the kernel type are proposed and their asymptotic properties are studied using different criteria. Rates of convergence are also provided. Performance of the estimators are examined in a simulation study, showing encouraging results. This analysis should be useful to researchers in the field and to anyone who may need to study this subject. Bestandsnummer des Verkäufers 9783838317458

Bibliografische Details

Titel: Nonparametric Statistics for Diffusion ...

Verlag: LAP LAMBERT Academic Publishing

Erscheinungsdatum: 2009

Einband: Taschenbuch

Zustand: Neu

Über diesen Titel

Reseña del editor:

Diffusion processes are widely used in many applied disciplines, such as biology, physics and financial mathematics. From the applied perspective multivariate diffusions are more interesting than scalar ones since only multidimensional models can describe the evolution of variables which interact among themselves. It is therefore very important to be able to identify such models starting from the observed data. However, while the scalar case has been widely studied, there are very few results for the multidimensional problem since these models present greater difficulties. This work provides a first insight into the problem of identification of multidimensional diffusions: the purpose is to estimate density and drift by the observation of a trajectory of a d-dimensional homogeneous diffusion process with a unique invariant density. Estimators of the kernel type are proposed and their asymptotic properties are studied using different criteria. Rates of convergence are also provided. Performance of the estimators are examined in a simulation study, showing encouraging results. This analysis should be useful to researchers in the field and to anyone who may need to study this subject.