On the Hawkes Process with Different Exciting Functions

2014/03/05 by Behzad Mehrdad, Lingjiong Zhu, Mehrdad, Behzad +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Economics and business #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Risk Management (q-fin.RM) #Trading and Market Microstructure (q-fin.TR)

paper · pdf · doi:10.48550/arxiv.1403.0994

openalex publication_date 2014/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has immigration-birth representation. Based on that, Fierro et al. recently introduced a generalized linear Hawkes model with different exciting functions. In this paper, we study the convergence to equilibrium, large deviation principle, and moderate deviation principle for this generalized model. This model also has connections to the multivariate linear Hawkes process. Some applications to finance are also discussed.

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