Abstract
The Hawkes process is a self-exciting point process with clustering effect whose intensity depends on its entire past history. It has wide applications in neuroscience, finance, and many other fields. In this paper we obtain a functional central limit theorem for the nonlinear Hawkes process. Under the same assumptions, we also obtain a Strassen's invariance principle, i.e. a functional law of the iterated logarithm.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference16 articles.
1. [15] Zhu L. (2012). Large deviations for Markovian nonlinear Hawkes Processes. Available at http://arxiv.org/abs/1108.2432v2.
2. [14] Liniger T. (2009). Multivariate Hawkes Processes. Doctoral Thesis, ETH.
3. [13] Karabash D. and Zhu L. (2013). Limit theorems for marked Hawkes processes with application to a risk model. Available at http://arxiv.org/abs/1211.4039v2.
4. An Introduction to the Theory of Point Processes
5. A dynamic contagion process
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