期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2015
卷号：XII
页码：477-489
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：In this work, we prove functional laws of large numbers and centrallimit theorem for an extension of the classical multivariate Hawkes process, whichassumes the clusters of the process are generated by di erent exciting functions.Namely, by rescaling this process, we prove laws of large numbers for the processesassociated to the extension of this Hawkes process. Also, a central limit theoremfor this normalized process is proved and a type Donsker theorem is showed whenunpredictable marks of the process are considered.
关键词：functional central limit theorem; clustering e ect; law of large num-;bers; unpredictable marks.
