# Student Probability Seminar

#### Asymptotics for Nonlinear Hawkes Processes

**Speaker:**
Ling Zhu

**Location:**
Warren Weaver Hall 1314

**Date:**
Thursday, April 11, 2013, 3:30 p.m.

**Synopsis:**

The Hawkes process is a simple point process that has long memory, clustering effect, self-exciting property and is in general non-Markovian. The future evolution of a self-exciting point process is influenced by the timing of the past events. There are applications in finance, neuroscience, DNA modeling, seismology, sociology, criminology and many other fields. We start with some known results about both linear and nonlinear Hawkes processes. Then, we will drop the usual assumptions on the nonlinear Hawkes process and categorize it into different regimes, i.e. sublinear, sub-critical, critical, super-critical and explosive regimes. We show some recent results on the different time asymptotics in different regimes and obtain other properties as well..