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Long-range Dependence trough Gamma-mixedOrnstein-Uhlenbeck Process


 
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1. Title Title of document Long-range Dependence trough Gamma-mixedOrnstein-Uhlenbeck Process
 
2. Creator Author's name, affiliation, country E. Igloi; L. Kossuth University
 
2. Creator Author's name, affiliation, country G. Terdik; L. Kossuth University
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Stationarity,Long-range dependence, Spectral representation,Ornstein--Uhlenbeck process,Aggregational model, Stochastic differentialequation, Fractional Brownianmotion input, Heart rate variability.
 
3. Subject Subject classification 60F, 60H, 92Cxx.
 
4. Description Abstract The limit process of aggregational models---(i) sum of random coefficient AR(1) processes with independent Brownian motion (BM) inputs and (ii) sum of AR(1) processes with random coefficients of Gamma distribution and with input of common BM's,---proves to be Gaussian and stationary and its transfer function is the mixture of transfer functions of Ornstein--Uhlenbeck (OU) processes by Gamma distribution. It is called Gamma-mixed Ornstein--Uhlenbeck process ($\Gamma\mathsf{MOU}$). For independent Poisson alternating $0$-$1$ reward processes with proper random intensity it is shown that the standardized sum of the processes converges to the standardized $\Gamma\mathsf{MOU}$ process. The $\Gamma\mathsf{MOU}$ process has various interesting properties and it is a new candidate for the successful modelling of several Gaussian stationary data with long-range dependence. Possible applications and problems are also considered.
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 1999-09-15
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/53
 
10. Identifier Digital Object Identifier 10.1214/EJP.v4-53
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 4
 
12. Language English=en en
 
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