Using Renewal Processes to Generate Long-Range Dependence and High Variability
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.
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