| Título: | Long-range Dependence trough Gamma-mixedOrnstein-Uhlenbeck Process |
| Autores: |
Igloi, E.; L. Kossuth University Terdik, G.; L. Kossuth University |
| Fecha: | 1999-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Mathematics Stationarity,Long-range dependence, Spectral representation,Ornstein--Uhlenbeck process,Aggregational model, Stochastic differentialequation, Fractional Brownianmotion input, Heart rate variability. 60F, 60H, 92Cxx. |
| Descripción: | 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. |
| Idioma: | Inglés |
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