TY - JOUR
T1 - Central limit theorem for nonlinear hawkes processes
AU - Zhu, Lingjiong
PY - 2013/9
Y1 - 2013/9
N2 - The Hawkes process is a self-exciting point process with clustering effect whose intensity depends on its entire past history. It has wide applications in neuroscience, finance, and many other fields. In this paper we obtain a functional central limit theorem for the nonlinear Hawkes process. Under the same assumptions, we also obtain a Strassen's invariance principle, i.e. a functional law of the iterated logarithm.
AB - The Hawkes process is a self-exciting point process with clustering effect whose intensity depends on its entire past history. It has wide applications in neuroscience, finance, and many other fields. In this paper we obtain a functional central limit theorem for the nonlinear Hawkes process. Under the same assumptions, we also obtain a Strassen's invariance principle, i.e. a functional law of the iterated logarithm.
KW - Central limit theorem
KW - Functional central limit theorem
KW - Hawkes process
KW - Point process
KW - Self-exciting process
UR - http://www.scopus.com/inward/record.url?scp=84885164766&partnerID=8YFLogxK
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U2 - 10.1239/jap/1378401234
DO - 10.1239/jap/1378401234
M3 - Article
AN - SCOPUS:84885164766
VL - 50
SP - 760
EP - 771
JO - Journal of Applied Probability
JF - Journal of Applied Probability
SN - 0021-9002
IS - 3
ER -