Rozhkova, A. V.

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Tomsk State University Repository

Томский государственный университет Механико-математический факультет      Молодежная научная конференция «Все грани математики и механики»  24–30 апреля 2015 г.    Сборник тезисов     Томск – 2015  79  Prediction with guaranteed accuracy for Ornstein-Uhlenbeck process Rozhkova A.V. Advisor: professor, Dr. Vasiliev Tomsk State University E-mail: svetlana-rozh@mail.ru  The process ( )x t is supposed to be stable and the parameter [ ; ]a     with known  and :                                          ( ) ( ) ( )dx t a x t dt dw t                             (1) The problem is to construct the predictions of the process ( )x t with the given mean square accuracy by discrete-time observationsn nhy x , 0,n T h ; h  is a discretisation step. Using the solution of the process (1) we obtain the autoregressive-type equation for observationsny : 1n n ny y   , where ahe   and n  are i.i.d. Gaussian noises with finite variance. According to the condition on the minimal value of the variance equals to:  22 ( )21, ( 1)2t nhenh t n h     . If the parameter a  is known, the optimal predictor 0 ( )x t  of ( )x t  is defined: 0 ( )( ) , ( 1)a t nh nx t e y nh t n h    . For the definition of adaptive predictor (the case of unknown a ) the parameter a should be replaced on some estimator. We use the truncated estimator   01 , 0n na a  , constructed in [1] by observations   0,k k nhy   , and having the property:  2, 1,nCM a a n T hn   .  It is proved that adaptive predictor ( )ˆ( ) , ( 1)na t nh nx t e y nh t n h     is closed to the optimal one in the following non-asymptotic sense:                               20ˆ( ) ( ) , 0,CM x t x t t Tt   .  References  Vasiliev\,V.\,A. A truncated estimation method with guaranteed accuracy // Annals of the 1Institute of Statistical Mathematics. 2013 . Vol. 66, Iss. 1. P. 141-163  

Prediction with guaranteed accuracy for Ornstein-Uhlenbeck process

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Prediction with guaranteed accuracy for Ornstein-Uhlenbeck process

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