Limit theorems for discrete Hawkes processes. (English) Zbl 1315.60058
Summary: We consider a discrete time Hawkes process which is a class of \(g\)-functions. The limit theorems for continuous time Hawkes processes are well known and studied by many authors. In this paper, we study the limit theorems for discrete time Hawkes processes. In particular, we obtain the law of large numbers, the central limit theorem and the invariance principle.
MSC:
| 60G55 | Point processes (e.g., Poisson, Cox, Hawkes processes) |
| 60F05 | Central limit and other weak theorems |
| 60F15 | Strong limit theorems |
| 60F17 | Functional limit theorems; invariance principles |
Keywords:
discrete Hawkes processes; self-exciting processes; central limit theorem; law of large numbers; invariance principleReferences:
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