# Student Probability Seminar

#### Stability of Hawkes Process

**Speaker:**
Dmytro Karabash

**Location:**
Warren Weaver Hall 512

**Date:**
Friday, October 28, 2011, 3:30 p.m.

**Synopsis:**

For Hawkes process, long-memory point process \(P\) with intensity \(\lambda \big(g_0(t)+ \sum_{\tau<t, \tau \in P} h(t-\tau) \big)\) at time \(t\) some existence and stability properties are observed. The main result is that under suitable conditions on parameters we show existence of unique invariant distribution of the process; the main difference with previous results is that Lipschitz condition of \(\lambda\) is not required. These methods also provide estimates on the difference at later times of the distributions of the process starting from two different initial conditions. Link to pre-arXiv preprint is here.