@article{EJP53,
author = {E. Igloi and G. Terdik},
title = {Long-range Dependence trough Gamma-mixedOrnstein-Uhlenbeck Process},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {4},
year = {1999},
keywords = {Stationarity,Long-range dependence, Spectral representation,Ornstein--Uhlenbeck process,Aggregational model, Stochastic differentialequation, Fractional Brownianmotion input, Heart rate variability.},
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.},
pages = {no. 16, 1-33},
issn = {1083-6489},
doi = {10.1214/EJP.v4-53},
url = {http://ejp.ejpecp.org/article/view/53}}