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Diyala Journal For Pure Science

Scientific Refereed Journal Published By College of Science - University of Diyala

 

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djps.1302.176A

Diyala Journal For Pure Sciences DJPS

ISRA Impact Factor:3.715

P- ISSN:2222-8373, E-ISSN:2518-9255

Volume 13, Issue 2, Part 1 , April. 2017

 

 

Linear Filtering of the Sum of Two Known Stochastic Processes

 

Sayran Hmza Raheem

 

Year: 2017, Volume: 13, Issue: 2, Part: 1

 

Pages: 116-131, DOI: http://dx.doi.org/10.24237/djps.1302.176A

 

Language: English

 

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Abstract          


The linear filtering got the great attention of statisticians and applied mathematician; therefore the present study aims at finding the linear filtering of stationary stochastic process and that is when we know the values of the sum of two stochastic processes at all moments of the time and when   and this requires us to know the spectral density function     for the stochastic processes. In this paper, we opted to take two cases after giving the necessary definitions for all important terms and finding the spectral density function for each stochastic processes (Poisson process and Wide Sense Markov process)  ; in the first case we supposed that both of the stochastic processes are stationary Poisson processes  and after finding the linear filtering we compute the mean square filtering error ;and in second case we suppose one of the stochastic process is Poisson process and the other is wide sense Markov process also in this case we find the mean square filtering error .

 

Keywords: linear Filtering; Stochastic Process; Wide Sense; stationary Markov process 

 

 

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