All Title Author
Keywords Abstract

Mathematics  2011 

Large deviations for Markovian nonlinear Hawkes processes

DOI: 10.1214/14-AAP1003

Full-Text   Cite this paper   Add to My Lib

Abstract:

Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, neuroscience and many other fields. In this paper, we study the large deviations for nonlinear Hawkes processes. The large deviations for linear Hawkes processes has been studied by Bordenave and Torrisi. In this paper, we prove first a large deviation principle for a special class of nonlinear Hawkes processes, that is, a Markovian Hawkes process with nonlinear rate and exponential exciting function, and then generalize it to get the result for sum of exponentials exciting functions. We then provide an alternative proof for the large deviation principle for a linear Hawkes process. Finally, we use an approximation approach to prove the large deviation principle for a special class of nonlinear Hawkes processes with general exciting functions.

Full-Text

comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

微信:OALib Journal