<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We study exact optimal designs for processes governed by mean- -reversion stochastic differential equations with a time dependent volatility and known mean-reversion speed. It turns out that any mean-reversion It¯o process has a product covariance structure.We prove the existence of a nondegenerate optimal sampling design for the parameter estimation and derive the information matrix corresponding to the observation of the full path. The results are demonstrated on a process with exponential volatility.</p></abstract>

We study exact optimal designs for processes governed by mean- -reversion stochastic differential equations with a time dependent volatility and known mean-reversion speed. It turns out that any mean-reversion It¯o process has a product covariance structure.We prove the existence of a nondegenerate optimal sampling design for the parameter estimation and derive the information matrix corresponding to the observation of the full path. The results are demonstrated on a process with exponential volatility.

Planning of experiments for a nonautonomous ornstein-uhlenbeck process

Department of Applied Mathematics and Statistics Faculty of Mathematics, Physics and Informatics Comenius University in Bratislava Mlynsk´a dolina SK–842-48 Bratislava SLOVAKIA

Tatra Mountains Mathematical Publications

{"article-title":"Planning of experiments for a nonautonomous ornstein-uhlenbeck process"}

We study exact optimal designs for processes governed by mean- -reversion stochastic differential equations with a time dependent volatility and known...

Planning of experiments for a nonautonomous ornstein-uhlenbeck process

Published Online: Nov 13, 2012

Page range: 101 - 113

DOI: https://doi.org/10.2478/v10127-012-0011-2

Keywords
exact design, product covariance structure, It¯o stochastic differential equation, estimation, asymptotic information matrix, efficiency.

This content is open access.

Planning of experiments for a nonautonomous ornstein-uhlenbeck process

Published Online: Nov 13, 2012

Page range: 101 - 113

DOI: https://doi.org/10.2478/v10127-012-0011-2

Keywordsexact design, product covariance structure, It¯o stochastic differential equation, estimation, asymptotic information matrix, efficiency.

This content is open access.

Keywords
exact design, product covariance structure, It¯o stochastic differential equation, estimation, asymptotic information matrix, efficiency.