# 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.