Abstract: In this talk, we present convergence results for Poisson cluster point processes driven by heavy-tailed components. The stated convergence takes place on a space of Borel measures defined on an underlying space which is punctured, which allows us to interpret it as regular variation of the point process. Additionally, we examine the convergence of functionals of these processes within the space of càdlàg functions, employing the M1-topology. Finally, we provide a Compound Poisson approximation for the sequence of point processes. This is a joint work with Olivier Wintenberger.
Limiting results and large deviation principles for Poisson cluster processes
16.01.2025 13:00 - 14:30
Organiser:
A. Carrance, W. Da Silva, K. Ryan
Location: