4 papers · 1 filter
An Exchangeable Pair-Hawkes Reference Model and a Cumulant Obstruction for Hard-Sphere Collision Statistics
Luis Iván Hernández Ruíz
Collision counts in a dilute gas of hard particles reflect the dependence between successive encounters. We study whether these fluctuations can be represented by a positive linear…
Results for convergence rates associated with renewal processes
Luis Iván Hernández Ruíz
Via a coupling argument, it is proved that the solution to a renewal equation has a power law decay rate in the case of a spread out interarrival distribution. By the regenerative…
Law of large numbers and central limit theorem for renewal Hawkes processes
Luis Iván Hernández Ruíz
A uniform law of large numbers and a central limit theorem are established via a martingale approach for a univariate Hawkes process with immigration given by a renewal process. Th…
A cluster representation of the renewal Hawkes process
Luis Iván Hernández Ruíz, Kouji Yano
A cluster representation for a Hawkes process with renewal immigration is obtained. The centre and satellite processes are indicated as a renewal process and generalized branching…