ﻻ يوجد ملخص باللغة العربية
We modify ETAS models by replacing the Pareto-like kernel proposed by Ogata with a Mittag-Leffler type kernel. Provided that the kernel decays as a power law with exponent $beta + 1 in (1,2]$, this replacement has the advantage that the Laplace transform of the Mittag-Leffler function is known explicitly, leading to simpler calculation of relevant quantities.
In this work, we study the event occurrences of user activities on online social network platforms. To characterize the social activity interactions among network users, we propose a network group Hawkes (NGH) process model. Particularly, the observe
To extend several known centered Gaussian processes, we introduce a new centered mixed self-similar Gaussian process called the mixed generalized fractional Brownian motion, which could serve as a good model for a larger class of natural phenomena. T
In the last decade, Hawkes processes have received a lot of attention as good models for functional connectivity in neural spiking networks. In this paper we consider a variant of this process, the Age Dependent Hawkes process, which incorporates ind
We build and study a data-driven procedure for the estimation of the stationary density f of an additive fractional SDE. To this end, we also prove some new concentrations bounds for discrete observations of such dynamics in stationary regime.
We test three common information criteria (IC) for selecting the order of a Hawkes process with an intensity kernel that can be expressed as a mixture of exponential terms. These processes find application in high-frequency financial data modelling.