Some asymptotic results for nonlinear Hawkes processes |
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Authors: | Fuqing Gao Lingjiong Zhu |
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Institution: | 1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, People’s Republic of China;2. Department of Mathematics, Florida State University, 1017 Academic Way, Tallahassee, FL-32306, USA |
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Abstract: | Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this paper, we study fluctuations, large deviations and moderate deviations nonlinear Hawkes processes in a new asymptotic regime, the large intensity function and the small exciting function regime. It corresponds to the large baseline intensity asymptotics for the linear case, and can also be interpreted as the asymptotics for the mean process of Hawkes processes on a large network. |
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Keywords: | Corresponding author |
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