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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© 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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