Percolation theory of self-exciting temporal processes

Spectra of some self - exciting and mutually exciting point processes

In recent years methods of data analysis for point processes have received some attention, for example, by Cox & Lewis (1966) and Lewis (1964). In particular Bartlett (1963a, b) has introduced methods of analysis based on the point spectrum. Theoretical models are relatively sparse. In this paper the theoretical properties of a class of processes with particular reference to the point spectrum ...

MA3H2 Markov Processes and Percolation theory

The Field Theory Approach to Percolation Processes

We review the field theory approach to percolation processes. Specifically, we focus on the so-called simple and general epidemic processes that display continuous nonequilibrium active to absorbing state phase transitions whose asymptotic features are governed respectively by the directed (DP) and dynamic isotropic percolation (dIP) universality classes. We discuss the construction of a field ...

Latent Self-Exciting Point Process Model for Spatial-Temporal Networks

Social network data is generally incomplete with missing information about nodes and their interactions. Here we propose a spatialtemporal latent point process model that describes geographically distributed interactions between pairs of entities. In contrast to most existing approaches, we assume that interactions are not fully observable, and certain interaction events lack information about ...

Self-exciting point processes with applications in finance and medicine