Abstract
We explore here three types of convergence theorems involving the normalized partial sums of two random processes W = W(t) and V = V(t) indexed by the integers t = ...,−1, 0.1,... . W(t) is a stationary renewal reward process with large inter-renewal intervals, while V(t) is a non-stationary process that takes the value zero except at some rare instants t where it achieves extremely high values.
Research supported by the National Science Foundation grant ECS-80-15585.
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References
Ibragimov, I.A. and Linnik, Y.V. (1971). Independent and Stationary Sequences of Random Variables. Groningen: Wolters-Nordhoff.
Levy, J.B. (1983). High variability and long-range dependence: a modeling approach based on renewal sequences. M.S. thesis: Cornell University.
Mandelbrot, B.B. (1969). Long-run linearity, locally Gaussian processes, H-spectra, and infinite variances. International Economic Review, 10, 82–113.
Mandelbrot, B.B. (1982). The Fractal Geometry of Nature. San Francisco: W.H. Freeman Co.
Mandelbrot, B.B. and Taqqu, M.S. (1979). Robust R/S analysis of long-run serial correlation. Proceedings of the 42nd Session of the International Statistical Institute, Manila. Bulletin of the I.S.I., Vol. 48, Book 2, pp. 69–104.
Mijnheer, J.L. (1975). Sample Path Properties of Stable Processes. Mathematical Centre Tracts 59. Amsterdam: Mathematisch Centrum.
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© 1986 Springer Science+Business Media New York
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Taqqu, M.S., Levy, J.B. (1986). Using Renewal Processes to Generate Long-Range Dependence and High Variability. In: Eberlein, E., Taqqu, M.S. (eds) Dependence in Probability and Statistics. Progress in Probability and Statistics, vol 11. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4615-8162-8_3
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DOI: https://doi.org/10.1007/978-1-4615-8162-8_3
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4615-8163-5
Online ISBN: 978-1-4615-8162-8
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