Nonparametric Statistics for Diffusion Processes : The multidimensional case

Annamaria Bianchi

ISBN 10: 3838317459 / ISBN 13: 9783838317458

Editore: LAP LAMBERT Academic Publishing, 2009

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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. Codice articolo 9783838317458

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Titolo: Nonparametric Statistics for Diffusion ...

Casa editrice: LAP LAMBERT Academic Publishing

Data di pubblicazione: 2009

Legatura: Taschenbuch

Condizione: Neu

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Riassunto:

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.

L'autore:

Annamaria Bianchi, phD in Matematica e Statistica per le Scienze Computazionali (University of Milan) and Docteur en Sciences Mathématiques (University Paris 6). Since 2007 she is research assistant at the University of Bergamo. Her research fields are statistics for diffusions, M-quantile regression and small area estimation.