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