Scaling limits for INAR(∞) processes
Abstract
In this paper, we study law of large numbers, central limit theorem, large and moderate deviations for INAR(∞) processes, which as a special case, includes both discrete-time linear Hawkes process and INAR(1) process in the literature. Our results recover existing results on large and moderate deviations for the discrete-time Hawkes process as studied in Wang2 and for the INAR(1) process as in Yu.
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