Stochastic Filtering
Show full item record
Files in this item
Title:

Stochastic Filtering 
Author:

Yazigi, Adil

Contributor:

University of Helsinki, Faculty of Science, Department of Mathematics and Statistics 
Thesis level:

Master's thesis 
Abstract:

The stochastic filtering has been in general an estimation of indirectly observed states given observed data. This means that one is discussing conditional expected values as being one of the most accurate estimation, given the observations in the context of probability space. In my thesis, I have presented the theory of filtering using two different kind of observation process: the first one is a diffusion process which is discussed in the first chapter, while the third chapter introduces the latter which is a counting process. The majority of the fundamental results of the stochastic filtering is stated in form of interesting equations, such the unnormalized Zakai equation that leads to the KushnerStratonovich equation. The latter one which is known also by the normalized Zakai equation or equally by FujisakiKallianpurKunita (FKK) equation, shows the divergence between the estimate using a diffusion process and a counting process. I have also introduced an example for the linear gaussian case, which is mainly the concept to build the socalled KalmanBucy filter. As the unnormalized and the normalized Zakai equations are in terms of the conditional distribution, a density of these distributions will be developed through these equations and stated by Kushner Theorem. However, Kushner Theorem has a form of a stochastic partial differential equation that needs to be verify in the sense of the existence and uniqueness of its solution, which is covered in the second chapter. 
URI:

URN:NBN:fife201011032663
http://hdl.handle.net/10138/21308

Date:

20101005 
Copyright information:

This publication is copyrighted. You may download, display and print it for Your own personal use. Commercial use is prohibited. 
This item appears in the following Collection(s)
Show full item record